-WiP- John Herold's Project

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The Android/iPhone App Alchemy

Alchemy is an interesting game made for Android and iPhone that involves the combination of "elements" to produce a new element (or in some cases more than one). The object of the game is to "create" all of the elements that currently exist in the game (which is right now around 380) using only the base elements you are provided with at the start of a new game. By combining these basic elements you can create new elements, which then can then be used to create even more elements by combining them with either a basic elemnt or another element created from them. Throughout my exploration of this game I have discovered various areas of discrete math that can be seen in the game including: recursion, sets and set theory, combinatorics, and even the concept of graphical trees can be seen in the game.

The Basics of How to Play

In the start of the game you have only 4 elements you can choose to combine:

  • Earth
  • Fire
  • Water
  • Air

These four elements appear on the screen on what is called your workspace, which is where you will lay out all the elements when you are working on combining them into new elements. The way you combine these basic elements by dragging and dropping one onto another. If these elements "react" to create something then a new element will be produced and will appear on the screen in place of the two elements you used to create it. Note that you can only combine two elements at a time, but it is possible to get more than one element out of the combination. If you make a new element it is also now added to your "toolbox" which you can take elements out of at any time to place onto your active workspace.

Lets look at an example of a combination:

We start with fire, earth, wind, and water...
so lets combine earth and water and see if we get something:

Earth + Water ==> Swamp

We made swamp! Our first creation, isn't it a beauty?

As you can see the gameplay is pretty simple: you pick two elements you think might combine to make something cool and interesting (or maybe not so interesting or expected) and test them by dropping them on each other. If the reaction yields products, you now have those to use in further combinations. If they don't react, well there isn't a penalty for that so you can keep trying with something else (Or the same two, but don't expect a different result).

Let's look at a series of combinations

We start with our basics and see what we can make after a few combinations:

1) Fire + Earth ==> Stone
2) Stone + Air ==> Sand
3) Earth + Water ==> Swamp
4) Sand + Swamp ==> Clay
5) Clay + Fire ==> Brick

So we can see that to make Brick in the game you need: Fire, Earth, Stone, Air, Sand, Water, Swamp, and Clay in your toolbox.

The game is interesting to play because it requires some thought, trial and error, and some organization if you hope to create all 380 elements from the starting 4.

One final aspect of gameplay to mention is that there are some elements that cannot be combined with any other element to produce further new elements. These elements are called "terminal elements" and you are notified by the game if you have created one of these so that you don't waste your time frustratingly trying to combine the element with every other element in the game for no result.

Recursion in Alchemy

While I was having fun experimenting with the game I discovered that recursion pops up when you are trying to figure out what elements you combined to make a particular element. For example, let's say you are trying to figure out what you need to combine to make the Electricity element. So you try and randomly experiment around combining various elements until you finally decide to look it up on a recipe website someone has made. You find that to make Electricity you need to combine Metals and Lightning. Okay, simple enough but wait - what makes Metals and Lightning? We can see that we have a recipe list that involves recursion. Your base cases are the four basic elements: Fire, Water, Earth, and Air. If an element is not one of those, it can be broken down further so continue to recurse back for each previous element combined until you have only basic elements. You will then have what I will call the "prime elemental factorization" of your element.

Looking at an example of how we would make Electricity:

Electricity <== Metals + Lightning

   Find out what makes Metals:
     Metals <== Stone + Fire (Fire is a basic element so we continue with Stone)
     
     Find out what makes Stone:
        Stone <== Fire + Earth (Both are basic so we are done)

So far we have: (Fire + Earth) + Fire ==> Metals,
continuing with the other element of Electricity:
   Find out what makes Lighting:
     Air + Fire (Air is basic, Fire is basic, we're done)

Now, no further elements need to be broken down so we combine what we have
to form an equation for Electriciy:
[(Fire + Earth) + Fire] + (Air + Fire) ==> Electricity

Trees in Alchemy

When looking at Alchemy and the elements created I began to see a structure that was involved in a particular element. Since exactly two elements are combined to create a particular non-basic element, you can represent this element's recipe by creating a tree where the root is the element of interest. Also, since the root and the root/parent of every subtree in the tree can at most have 2 children (since you can't combine 3 or more elements to make any element) the tree is binary in nature. The leaf nodes of the tree will be basic elements since they cannot be broken down further.


Combinatorics in Alchemy

How can you have a game about combining things together that doesn't involve at least some basic combinatorics! In Alchemy you can clearly see that if every element had to have a combination with at least one element (including itself) to produce a new unique element- that there would would be an infinite amount of elements because each new element we created would have to combine further to make another new unique element, and that one another one.... and so on. Fortunately for the programmers of Alchemy, that isn't the case as there exists terminal elements and there exists only a finite number of possible combinations and elements.

Let's look at a simple example:

Since there is 380 elements currently in the game, we can consider all elements in the game as a set. Say we want t figure out how many possible ways you could combine two different elements in this set together: We have 380 elements, taking 2 at a time to combine without order being important (Water + Earth makes the same swamp as Earth + Water) we would have \frac{380!}{(380-2)!}.(380 permute 2) or 72,010 possible ways you could try to combine elements to make new ones. Thankfully not every element combines with every other element!

You could use combinatorics and probability to find things like the probability that combining two random elements would produce a new element given the total number of elements in the game, the number of terminal elements, and the recipe list for which elements combine with which other elements.

A Simulation of "A Game of Life"

I am expanding on this project by taking the suggestion to create a "game of life" in which elements are allowed to randomly (psuedo-randomly as a computer is generating the random numbers) combine. The results are observed to see what kinds of elements arise out of the basic four: Air, Water, Fire, and Earth. I decided to run tests of different size number of attempted combinations starting with 1,000 then running it with 10,000 100,000 and finally 1,000,000 random combinations.

The basic way the program runs is first it loads in the recipies from a .txt file and puts each line of the file into an array of Strings (each line represents a combination of two elements to produce another element). This array is used to check whether two randomly chosen elements will combine to form something new. I used a list of about 270 elements from the original game and formated them as such in the file:

[Element Produced]= [Element1] + [Element2]

Where the new element preceeds the equals sign and the two that combine to create it follow separated by the plus sign. An asterisk appended to the end of the [Element Produced] name is used to denote a terminal element (one that can't be combined further).

An array list is used to hold and keep track of all elements that have been created througout the course of running the program and simulating the random combinations. Each time a new element is created through a random combination, it is added to the array list and can be potentially picked the next round of combinations.

The general algorithm for the main program is this:

  1. Populate the array list of elements with the basic four: Air, Water, Earth, and Fire.
  2. Read in the list of possible combinations from the .txt file (combinations.txt)
  3. Add each possible combination to an array of strings to be passed to the method that checks if the two randomly chosen elements combine to make one or more elements.
  4. Randomly select two elements from the array list of currently created elements and call the combineWith() function.
  5. Recieve back a linked list of elements (if any) the elements combined to create
  6. Check and see if any of the elements aren't already in our array list of currently created elements and if not add them to it so the next run of the loop it can possibly be chosen to combine with something as well.
  7. Output any new elements formed with the number of combinations that it took to create the element.
  8. Finally print out how many elements were created out of how many possible before terminating the program.

Here is the java method for combining two elements:

   // Takes another element and an array of strings containing the recipies for elements as paramters
   public LinkedList<Element> combineWith(Element otherElement, String recipeList[])
   {
       String currentRecipe[];
       LinkedList<Element> newElements = new LinkedList<Element>();
       for(int i = 0; i < recipeList.length; i++)
       {
           currentRecipe = recipeList[i].split("[+=]");
           if( (currentRecipe[1].trim().equalsIgnoreCase(name) && currentRecipe[2].trim().equalsIgnoreCase(otherElement.getName())) || (currentRecipe[2].trim().equalsIgnoreCase(name) && currentRecipe[1].trim().equalsIgnoreCase(otherElement.getName())) )
           {
               // There is a recipe for these two elements, this is a valid combination
               String newElementName = currentRecipe[0];
               boolean isTerminal = false;
               // Check if the element is terminal (denoted by an asterisk in the name)
               if(newElementName.contains("*"))
               {
                   isTerminal = true;
                   newElementName = newElementName.replace("*", "");
               }
               Element newElement = new Element(newElementName, isTerminal); // Create the new element
               newElements.add(newElement);
           }
       }
       return newElements; // return the linked list of new elements created (if any) in this combination
   }

Here is the output of the 1,000 attempted combinations run:

run:
Steam was created after 1 combinations (Water + Air)
Energy was created after 2 combinations (Fire + Air)
Geyser was created after 4 combinations (Earth + Steam)
Dust was created after 8 combinations (Earth + Air)
Swamp was created after 15 combinations (Water + Earth)
Alcohol was created after 19 combinations (Water + Fire)
Vodka was created after 34 combinations (Water + Alcohol)
Wind was created after 45 combinations (Air + Air)
Cloud was created after 53 combinations (Air + Steam)
Storm was created after 56 combinations (Energy + Air)
Mud was created after 64 combinations (Water + Dust)
Sky was created after 66 combinations (Air + Cloud)
Gunpowder was created after 95 combinations (Fire + Dust)
Typhoon was created after 100 combinations (Water + Storm)
Molotov Cocktail was created after 189 combinations (Fire + Alcohol)
Lava was created after 291 combinations (Earth + Fire)
Stone was created after 322 combinations (Air + Lava)
Life was created after 457 combinations (Energy + Swamp)
Metal was created after 525 combinations (Fire + Stone)
Algae was created after 528 combinations (Life + Water)
Rust was created after 553 combinations (Water + Metal)
Pressure was created after 570 combinations (Earth + Earth)
Sand was created after 584 combinations (Stone + Water)
Clay was created after 603 combinations (Sand + Swamp)
Volcano was created after 618 combinations (Lava + Pressure)
Egg was created after 682 combinations (Stone + Life)
Mite was created after 724 combinations (Dust + Life)
Bird was created after 737 combinations (Air + Egg)
Mushroom was created after 794 combinations (Earth + Algae)
Golem was created after 806 combinations (Life + Clay)
Mold was created after 899 combinations (Mud + Mushroom)
Glass was created after 902 combinations (Fire + Sand)
Metal Golem was created after 930 combinations (Metal + Life)
Turtle was created after 936 combinations (Sand + Egg)
Fire Elemental was created after 963 combinations (Fire + Life)
Silicon was created after 994 combinations (Pressure + Sand)
After 1000 simulated random combinations, 
36 new elements were created out of the total possible 266.

Here is output from the 10,000 attemped combinations run:

run:
Steam was created after 1 combinations (Water + Air)
Alcohol was created after 2 combinations (Water + Fire)
Molotov Cocktail was created after 3 combinations (Alcohol + Fire)
Swamp was created after 4 combinations (Earth + Water)
Energy was created after 5 combinations (Fire + Air)
Cloud was created after 12 combinations (Steam + Air)
Lava was created after 23 combinations (Fire + Earth)
Dust was created after 24 combinations (Air + Earth)
Gunpowder was created after 31 combinations (Dust + Fire)
Stone was created after 35 combinations (Lava + Air)
Sky was created after 39 combinations (Cloud + Air)
Vodka was created after 65 combinations (Water + Alcohol)
Life was created after 68 combinations (Energy + Swamp)
Fire Elemental was created after 69 combinations (Life + Fire)
Sand was created after 72 combinations (Water + Stone)
Desert was created after 81 combinations (Sand + Sand)
Algae was created after 89 combinations (Water + Life)
Clay was created after 96 combinations (Sand + Swamp)
Mite was created after 110 combinations (Life + Dust)
Golem was created after 114 combinations (Life + Clay)
Wind was created after 117 combinations (Air + Air)
Egg was created after 154 combinations (Life + Stone)
Lava Golem was created after 157 combinations (Lava + Life)
Pressure was created after 163 combinations (Earth + Earth)
Volcano was created after 191 combinations (Pressure + Lava)
Brick was created after 227 combinations (Fire + Clay)
Silicon was created after 240 combinations (Pressure + Sand)
Bacteria was created after 259 combinations (Life + Swamp)
Iodine was created after 269 combinations (Algae + Fire)
Beach was created after 304 combinations (Sand + Water)
Mushroom was created after 395 combinations (Earth + Algae)
Sulfur was created after 398 combinations (Bacteria + Swamp)
Turtle was created after 420 combinations (Egg + Sand)
Metal was created after 467 combinations (Fire + Stone)
Rust was created after 673 combinations (Metal + Water)
Electricity was created after 696 combinations (Metal + Energy)
Boiler was created after 753 combinations (Metal + Steam)
Glass was created after 773 combinations (Fire + Sand)
Storm was created after 876 combinations (Energy + Air)
Omelette was created after 898 combinations (Egg + Fire)
Flu was created after 962 combinations (Air + Bacteria)
Petri Dish was created after 976 combinations (Bacteria + Glass)
Plankton was created after 1007 combinations (Water + Bacteria)
Dam was created after 1016 combinations (Brick + Water)
Hydrogen was created after 1133 combinations (Electricity + Water)
Oxygen was created after 1133 combinations (Electricity + Water)
Thunderstorm was created after 1273 combinations (Storm + Electricity)
Vinegar was created after 1324 combinations (Alcohol + Oxygen)
Dinosaur was created after 1386 combinations (Egg + Earth)
Moss was created after 1508 combinations (Swamp + Algae)
Chicken was created after 1560 combinations (Egg + Life)
Hourglass was created after 1688 combinations (Sand + Glass)
Typhoon was created after 1729 combinations (Storm + Water)
Fossil was created after 1883 combinations (Dinosaur + Earth)
Worm was created after 2019 combinations (Plankton + Earth)
Fern was created after 2134 combinations (Moss + Swamp)
Lightning Rod was created after 2237 combinations (Metal + Thunderstorm)
Bird was created after 2292 combinations (Air + Egg)
Lichen was created after 2306 combinations (Mushroom + Algae)
Metal Golem was created after 2360 combinations (Life + Metal)
Geyser was created after 2547 combinations (Steam + Earth)
Shells was created after 2596 combinations (Plankton + Stone)
Light bulb was created after 2608 combinations (Glass + Electricity)
Airplane was created after 2629 combinations (Metal + Bird)
Light was created after 2677 combinations (Light bulb + Electricity)
Lamp was created after 2718 combinations (Glass + Fire)
Lava Lamp was created after 2806 combinations (Lamp + Lava)
Zombie was created after 3304 combinations (Fossil + Life)
Piesiosauria was created after 3337 combinations (Dinosaur + Water)
Snail was created after 3360 combinations (Worm + Shells)
Tequila was created after 3401 combinations (Alcohol + Worm)
Sandstorm was created after 3520 combinations (Storm + Sand)
Seed was created after 3862 combinations (Sand + Life)
Snake was created after 3899 combinations (Swamp + Worm)
Oxyhydrogen was created after 3966 combinations (Oxygen + Hydrogen)
Butterfly was created after 4154 combinations (Worm + Air)
Thunderbird was created after 4470 combinations (Bird + Storm)
Flying Dinosaur was created after 4596 combinations (Dinosaur + Air)
Avian Flu was created after 4810 combinations (Flu + Bird)
Phoenix was created after 4825 combinations (Bird + Fire)
Kerogen was created after 4878 combinations (Fossil + Pressure)
Ozone was created after 4886 combinations (Electricity + Oxygen)
Pearl was created after 5039 combinations (Sand + Shells)
Electric eel was created after 5190 combinations (Electricity + Snake)
1UP was created after 5433 combinations (Life + Mushroom)
Quetzalcoatl was created after 5942 combinations (Snake + Bird)
Fish was created after 6064 combinations (Plankton + Bacteria)
Electric ray was created after 6575 combinations (Fish + Electricity)
Limestone was created after 6896 combinations (Shells + Stone)
Dragon was created after 7089 combinations (Flying Dinosaur + Fire)
Lizard was created after 7811 combinations (Snake + Worm)
Mud was created after 9302 combinations (Water + Dust)
Beetle was created after 9700 combinations (Worm + Earth)
Scorpion was created after 9796 combinations (Sand + Beetle)
Cement was created after 9983 combinations (Limestone + Clay)
After 10000 simulated random combinations, 
95 new elements were created out of the total possible 266.

Here is the output of the 100,000 attempted combinations run:

run:
Dust was created after 1 combinations (Air + Earth)
Gunpowder was created after 2 combinations (Dust + Fire)
Wind was created after 3 combinations (Air + Air)
Swamp was created after 6 combinations (Earth + Water)
Mud was created after 11 combinations (Water + Dust)
Alcohol was created after 20 combinations (Fire + Water)
Lava was created after 31 combinations (Fire + Earth)
Stone was created after 41 combinations (Air + Lava)
Sand was created after 48 combinations (Stone + Water)
Steam was created after 58 combinations (Water + Air)
Geyser was created after 61 combinations (Earth + Steam)
Molotov Cocktail was created after 64 combinations (Fire + Alcohol)
Cloud was created after 107 combinations (Air + Steam)
Energy was created after 115 combinations (Fire + Air)
Vodka was created after 117 combinations (Alcohol + Water)
Clay was created after 121 combinations (Swamp + Sand)
Metal was created after 186 combinations (Stone + Fire)
Pressure was created after 200 combinations (Earth + Earth)
Boiler was created after 204 combinations (Metal + Steam)
Glass was created after 275 combinations (Sand + Fire)
Life was created after 290 combinations (Energy + Swamp)
Beach was created after 293 combinations (Sand + Water)
Brick was created after 319 combinations (Fire + Clay)
Hourglass was created after 339 combinations (Sand + Glass)
Fire Elemental was created after 378 combinations (Life + Fire)
Egg was created after 382 combinations (Stone + Life)
Bird was created after 385 combinations (Egg + Air)
Chicken was created after 400 combinations (Egg + Life)
Airplane was created after 430 combinations (Metal + Bird)
Turtle was created after 465 combinations (Egg + Sand)
Mite was created after 489 combinations (Life + Dust)
Algae was created after 496 combinations (Life + Water)
Electricity was created after 583 combinations (Metal + Energy)
Mushroom was created after 627 combinations (Algae + Earth)
Omelette was created after 629 combinations (Fire + Egg)
Lava Golem was created after 642 combinations (Life + Lava)
Volcano was created after 665 combinations (Lava + Pressure)
Hydrogen was created after 674 combinations (Water + Electricity)
Oxygen was created after 674 combinations (Water + Electricity)
Desert was created after 724 combinations (Sand + Sand)
Lichen was created after 743 combinations (Algae + Mushroom)
Bacteria was created after 855 combinations (Life + Swamp)
Sky was created after 877 combinations (Cloud + Air)
Golem was created after 902 combinations (Clay + Life)
Light bulb was created after 905 combinations (Electricity + Glass)
Iodine was created after 945 combinations (Fire + Algae)
Silicon was created after 962 combinations (Sand + Pressure)
Sulfur was created after 982 combinations (Bacteria + Swamp)
Oxyhydrogen was created after 1048 combinations (Oxygen + Hydrogen)
Storm was created after 1070 combinations (Energy + Air)
Typhoon was created after 1112 combinations (Storm + Water)
Light was created after 1122 combinations (Light bulb + Electricity)
Lamp was created after 1208 combinations (Fire + Glass)
Metal Golem was created after 1241 combinations (Metal + Life)
Plankton was created after 1360 combinations (Water + Bacteria)
Dam was created after 1469 combinations (Brick + Water)
Time was created after 1740 combinations (Life + Hourglass)
Thunderstorm was created after 1754 combinations (Storm + Electricity)
Phoenix was created after 1887 combinations (Bird + Fire)
Flu was created after 1905 combinations (Bacteria + Air)
Fish was created after 2245 combinations (Bacteria + Plankton)
Dinosaur was created after 2310 combinations (Earth + Egg)
Ozone was created after 2455 combinations (Oxygen + Electricity)
Avian Flu was created after 2458 combinations (Bird + Flu)
Worm was created after 2530 combinations (Earth + Plankton)
Mold was created after 2760 combinations (Mushroom + Mud)
Flying Dinosaur was created after 3160 combinations (Dinosaur + Air)
Tequila was created after 3497 combinations (Alcohol + Worm)
Moss was created after 3573 combinations (Algae + Swamp)
Fossil was created after 3618 combinations (Earth + Dinosaur)
Grass was created after 3620 combinations (Moss + Earth)
Butterfly was created after 3689 combinations (Worm + Air)
Rust was created after 3933 combinations (Water + Metal)
Thunderbird was created after 4217 combinations (Storm + Bird)
Reed was created after 4383 combinations (Grass + Swamp)
Zombie was created after 4423 combinations (Life + Fossil)
Seed was created after 4537 combinations (Sand + Life)
Beetle was created after 4655 combinations (Worm + Earth)
1UP was created after 4769 combinations (Life + Mushroom)
Fern was created after 4782 combinations (Moss + Swamp)
Piesiosauria was created after 4813 combinations (Dinosaur + Water)
Snake was created after 5382 combinations (Worm + Swamp)
Sandstorm was created after 5514 combinations (Storm + Sand)
Lizard was created after 5855 combinations (Worm + Snake)
Sushi was created after 6813 combinations (Algae + Fish)
Lightning Rod was created after 7030 combinations (Metal + Thunderstorm)
Scorpion was created after 7292 combinations (Sand + Beetle)
Tree was created after 7313 combinations (Earth + Seed)
Electric eel was created after 7636 combinations (Electricity + Snake)
Shells was created after 7963 combinations (Plankton + Stone)
Pearl was created after 8564 combinations (Sand + Shells)
Cactus was created after 9301 combinations (Desert + Tree)
Yoshi was created after 9663 combinations (1UP + Egg)
Vinegar was created after 9821 combinations (Oxygen + Alcohol)
Salamander was created after 9898 combinations (Lizard + Fire)
Frog was created after 9917 combinations (Lizard + Swamp)
Tobacco was created after 10264 combinations (Grass + Fire)
Christmas Tree was created after 11616 combinations (Tree + Light bulb)
Kerogen was created after 12245 combinations (Pressure + Fossil)
Electric ray was created after 12452 combinations (Electricity + Fish)
Snail was created after 12494 combinations (Shells + Worm)
Walking tree was created after 12616 combinations (Tree + Life)
Cochineal was created after 13135 combinations (Cactus + Beetle)
Ash was created after 13453 combinations (Fire + Tree)
Coal was created after 13453 combinations (Fire + Tree)
Uncut diamond was created after 14128 combinations (Coal + Pressure)
Lava Lamp was created after 14661 combinations (Lamp + Lava)
Flower was created after 14741 combinations (Seed + Water)
Petri Dish was created after 15503 combinations (Bacteria + Glass)
Ashtray was created after 15872 combinations (Glass + Ash)
Quetzalcoatl was created after 17386 combinations (Snake + Bird)
Bitumen was created after 17918 combinations (Pressure + Kerogen)
Steam engine was created after 18860 combinations (Coal + Boiler)
Beast was created after 19365 combinations (Earth + Lizard)
Panda was created after 19451 combinations (Tree + Beast)
Petroleum was created after 19713 combinations (Bitumen + Pressure)
Firefly was created after 19860 combinations (Beetle + Light)
Gasoline was created after 20097 combinations (Pressure + Petroleum)
Caviar was created after 22328 combinations (Fish + Fish)
Combustion Engine was created after 22621 combinations (Steam engine + Gasoline)
Ghost was created after 23211 combinations (Ash + Life)
Ectoplasm was created after 23544 combinations (Energy + Ghost)
Peat was created after 23573 combinations (Swamp + Tree)
Man was created after 23678 combinations (Life + Beast)
Mario was created after 24101 combinations (Man + 1UP)
Farmer was created after 24488 combinations (Man + Seed)
Idea was created after 24936 combinations (Light bulb + Man)
Fruit was created after 25155 combinations (Tree + Farmer)
Genie was created after 25400 combinations (Ghost + Lamp)
Hut was created after 25409 combinations (Man + Stone)
Limestone was created after 26214 combinations (Shells + Stone)
Alcoholic was created after 26216 combinations (Man + Alcohol)
Sick was created after 26539 combinations (Man + Flu)
Ceramics was created after 26830 combinations (Man + Clay)
Cement was created after 27437 combinations (Clay + Limestone)
Lime was created after 27817 combinations (Fire + Limestone)
Grove was created after 27968 combinations (Tree + Tree)
Berry was created after 28046 combinations (Fruit + Grass)
Sugar was created after 30356 combinations (Reed + Lime)
Scotch whiskey was created after 31148 combinations (Alcohol + Peat)
Hen Coop was created after 31907 combinations (Hut + Chicken)
Livestock was created after 33120 combinations (Beast + Man)
Tool was created after 33922 combinations (Metal + Man)
Arms was created after 35709 combinations (Tool + Metal)
Dragon was created after 35870 combinations (Fire + Flying Dinosaur)
Diamond was created after 36108 combinations (Tool + Uncut diamond)
Carmine was created after 36185 combinations (Fire + Cochineal)
Beaver was created after 36412 combinations (Dam + Beast)
Explosion was created after 37912 combinations (Gasoline + Fire)
Wood was created after 38629 combinations (Tool + Tree)
Milk was created after 39078 combinations (Man + Livestock)
Corpse was created after 41615 combinations (Fire + Man)
Caramel was created after 42359 combinations (Sugar + Fire)
Carbon Dioxide was created after 42671 combinations (Oxygen + Man)
Whale was created after 43744 combinations (Water + Beast)
Firearms was created after 44327 combinations (Arms + Gunpowder)
Concrete was created after 45354 combinations (Water + Cement)
Brick House was created after 45444 combinations (Brick + Concrete)
Boat was created after 45837 combinations (Wood + Water)
Grave was created after 45846 combinations (Corpse + Earth)
Soda water was created after 46870 combinations (Carbon Dioxide + Water)
Museum was created after 48021 combinations (Fossil + Brick House)
Smoke was created after 48298 combinations (Fire + Tobacco)
Pinocchio was created after 48541 combinations (Life + Wood)
Vulture was created after 48593 combinations (Bird + Corpse)
Paper was created after 49809 combinations (Tool + Reed)
Motorboat was created after 51348 combinations (Combustion Engine + Boat)
Zoo was created after 51350 combinations (Beast + Museum)
Arable was created after 52025 combinations (Tool + Earth)
Soldier was created after 52172 combinations (Firearms + Man)
Wheat was created after 53241 combinations (Arable + Seed)
Lightsaber was created after 54529 combinations (Arms + Light)
Forest was created after 56939 combinations (Grove + Grove)
Poison was created after 57117 combinations (Tool + Mushroom)
Coca-Cola was created after 59362 combinations (Soda water + Carmine)
Bear was created after 59890 combinations (Beast + Forest)
Cemetery was created after 60652 combinations (Grave + Grave)
Pig was created after 60972 combinations (Mud + Livestock)
Undead was created after 63388 combinations (Corpse + Zombie)
Beer was created after 63391 combinations (Wheat + Alcohol)
Grape was created after 63878 combinations (Wood + Earth)
Wine was created after 64729 combinations (Alcohol + Grape)
Sailor was created after 64776 combinations (Boat + Man)
Fat was created after 65287 combinations (Man + Pig)
Hunter was created after 65563 combinations (Man + Arms)
Soap was created after 66629 combinations (Fat + Ash)
Blood was created after 66680 combinations (Hunter + Beast)
Meat was created after 66680 combinations (Hunter + Beast)
Wool was created after 66680 combinations (Hunter + Beast)
Leech was created after 66933 combinations (Worm + Blood)
Warrior was created after 67249 combinations (Hunter + Arms)
Bacon was created after 68780 combinations (Fire + Pig)
Cigarettes was created after 68895 combinations (Tobacco + Paper)
Hospital was created after 69156 combinations (Brick House + Sick)
Hero was created after 69247 combinations (Dragon + Warrior)
Feather was created after 70614 combinations (Hunter + Bird)
Skyscraper was created after 72372 combinations (Brick House + Glass)
Barbecue was created after 73969 combinations (Fire + Meat)
Frankenstein was created after 74903 combinations (Corpse + Electricity)
Bar was created after 74938 combinations (Brick House + Beer)
Flour was created after 75702 combinations (Wheat + Stone)
Coffin was created after 76229 combinations (Wood + Corpse)
Poisoned Weapons was created after 77721 combinations (Poison + Arms)
Yogurt was created after 78206 combinations (Bacteria + Milk)
Manure was created after 78549 combinations (Livestock + Grass)
Lighthouse was created after 81517 combinations (Skyscraper + Light)
Dough was created after 82479 combinations (Water + Flour)
Knife was created after 83008 combinations (Meat + Tool)
Scarab was created after 83234 combinations (Manure + Beetle)
Bread was created after 85265 combinations (Dough + Fire)
Assassin was created after 86509 combinations (Man + Poisoned Weapons)
Diet was created after 86590 combinations (Man + Yogurt)
Book was created after 86751 combinations (Paper + Feather)
Firefighter was created after 88358 combinations (Hero + Fire)
Library was created after 88974 combinations (Book + Book)
Wooden ship was created after 89813 combinations (Boat + Wood)
Scientist was created after 90229 combinations (Library + Man)
Fisherman was created after 90674 combinations (Hunter + Fish)
Weevil was created after 90983 combinations (Flour + Beetle)
Wheel was created after 92249 combinations (Wood + Tool)
Stake was created after 94000 combinations (Knife + Wood)
Champagne was created after 96253 combinations (Wine + Soda water)
Scissors was created after 99029 combinations (Knife + Knife)
After 100000 simulated random combinations, 
223 new elements were created out of the total possible 266.

Here is the output of the 1,000,000 attempted combinations run:

run:
Alcohol was created after 1 combinations (Water + Fire)
Lava was created after 4 combinations (Fire + Earth)
Swamp was created after 5 combinations (Water + Earth)
Molotov Cocktail was created after 14 combinations (Fire + Alcohol)
Dust was created after 15 combinations (Earth + Air)
Mud was created after 18 combinations (Water + Dust)
Vodka was created after 25 combinations (Water + Alcohol)
Gunpowder was created after 26 combinations (Fire + Dust)
Energy was created after 38 combinations (Air + Fire)
Stone was created after 41 combinations (Lava + Air)
Pressure was created after 52 combinations (Earth + Earth)
Storm was created after 60 combinations (Air + Energy)
Steam was created after 65 combinations (Water + Air)
Geyser was created after 108 combinations (Earth + Steam)
Volcano was created after 117 combinations (Pressure + Lava)
Wind was created after 125 combinations (Air + Air)
Cloud was created after 136 combinations (Steam + Air)
Sky was created after 223 combinations (Cloud + Air)
Sand was created after 253 combinations (Stone + Water)
Life was created after 373 combinations (Energy + Swamp)
Seed was created after 400 combinations (Sand + Life)
Tree was created after 413 combinations (Earth + Seed)
Grove was created after 428 combinations (Tree + Tree)
Metal was created after 429 combinations (Fire + Stone)
Flower was created after 433 combinations (Water + Seed)
Mite was created after 438 combinations (Life + Dust)
Bacteria was created after 456 combinations (Swamp + Life)
Typhoon was created after 462 combinations (Storm + Water)
Plankton was created after 485 combinations (Bacteria + Water)
Lava Golem was created after 495 combinations (Lava + Life)
Shells was created after 613 combinations (Plankton + Stone)
Desert was created after 623 combinations (Sand + Sand)
Boiler was created after 676 combinations (Steam + Metal)
Rust was created after 679 combinations (Water + Metal)
Beach was created after 793 combinations (Water + Sand)
Fish was created after 830 combinations (Plankton + Bacteria)
Worm was created after 966 combinations (Plankton + Earth)
Beetle was created after 974 combinations (Worm + Earth)
Sulfur was created after 1088 combinations (Swamp + Bacteria)
Metal Golem was created after 1100 combinations (Metal + Life)
Algae was created after 1177 combinations (Life + Water)
Peat was created after 1182 combinations (Tree + Swamp)
Caviar was created after 1250 combinations (Fish + Fish)
Fire Elemental was created after 1252 combinations (Fire + Life)
Scotch whiskey was created after 1253 combinations (Peat + Alcohol)
Sushi was created after 1315 combinations (Algae + Fish)
Egg was created after 1339 combinations (Stone + Life)
Scorpion was created after 1442 combinations (Sand + Beetle)
Snake was created after 1465 combinations (Worm + Swamp)
Lizard was created after 1466 combinations (Snake + Worm)
Salamander was created after 1561 combinations (Lizard + Fire)
Frog was created after 1665 combinations (Swamp + Lizard)
Ash was created after 1677 combinations (Fire + Tree)
Coal was created after 1677 combinations (Fire + Tree)
Chicken was created after 1704 combinations (Life + Egg)
Bird was created after 1706 combinations (Air + Egg)
Omelette was created after 1843 combinations (Fire + Egg)
Electricity was created after 1893 combinations (Metal + Energy)
Butterfly was created after 1998 combinations (Air + Worm)
Snail was created after 2115 combinations (Worm + Shells)
Phoenix was created after 2386 combinations (Bird + Fire)
Pearl was created after 2445 combinations (Sand + Shells)
Hydrogen was created after 2477 combinations (Water + Electricity)
Oxygen was created after 2477 combinations (Water + Electricity)
Flu was created after 2578 combinations (Air + Bacteria)
Electric ray was created after 2691 combinations (Electricity + Fish)
Quetzalcoatl was created after 2693 combinations (Snake + Bird)
Avian Flu was created after 2755 combinations (Flu + Bird)
Limestone was created after 3039 combinations (Stone + Shells)
Beast was created after 3122 combinations (Lizard + Earth)
Oxyhydrogen was created after 3134 combinations (Oxygen + Hydrogen)
Clay was created after 3201 combinations (Swamp + Sand)
Electric eel was created after 3425 combinations (Electricity + Snake)
Iodine was created after 3547 combinations (Algae + Fire)
Vinegar was created after 3696 combinations (Oxygen + Alcohol)
Brick was created after 3896 combinations (Fire + Clay)
Whale was created after 3930 combinations (Beast + Water)
Tequila was created after 4036 combinations (Worm + Alcohol)
Panda was created after 4108 combinations (Beast + Tree)
Turtle was created after 4602 combinations (Egg + Sand)
Cactus was created after 4609 combinations (Tree + Desert)
Airplane was created after 4719 combinations (Bird + Metal)
Golem was created after 4755 combinations (Life + Clay)
Ghost was created after 4801 combinations (Life + Ash)
Dinosaur was created after 4910 combinations (Egg + Earth)
Thunderstorm was created after 5415 combinations (Storm + Electricity)
Lightning Rod was created after 6628 combinations (Metal + Thunderstorm)
Sandstorm was created after 6951 combinations (Storm + Sand)
Flying Dinosaur was created after 7025 combinations (Dinosaur + Air)
Ectoplasm was created after 7386 combinations (Ghost + Energy)
Forest was created after 7870 combinations (Grove + Grove)
Totora was created after 8258 combinations (Forest + Ghost)
Mushroom was created after 8312 combinations (Algae + Earth)
Man was created after 8764 combinations (Beast + Life)
Lichen was created after 9026 combinations (Algae + Mushroom)
Fossil was created after 9348 combinations (Earth + Dinosaur)
Alcoholic was created after 9550 combinations (Alcohol + Man)
Lime was created after 9658 combinations (Limestone + Fire)
Livestock was created after 9680 combinations (Man + Beast)
Carbon Dioxide was created after 9688 combinations (Man + Oxygen)
Kerogen was created after 10138 combinations (Pressure + Fossil)
Silicon was created after 10218 combinations (Sand + Pressure)
Bear was created after 10253 combinations (Beast + Forest)
Dragon was created after 10275 combinations (Flying Dinosaur + Fire)
Cement was created after 10287 combinations (Limestone + Clay)
Zombie was created after 10542 combinations (Fossil + Life)
Ceramics was created after 10553 combinations (Clay + Man)
Thunderbird was created after 10640 combinations (Storm + Bird)
Concrete was created after 10794 combinations (Cement + Water)
Steam engine was created after 10960 combinations (Boiler + Coal)
Soda water was created after 11744 combinations (Water + Carbon Dioxide)
Hut was created after 11930 combinations (Man + Stone)
Glass was created after 12109 combinations (Fire + Sand)
Lamp was created after 12239 combinations (Fire + Glass)
Moss was created after 13028 combinations (Swamp + Algae)
Walking tree was created after 13299 combinations (Tree + Life)
Petri Dish was created after 13982 combinations (Glass + Bacteria)
Corpse was created after 14052 combinations (Man + Fire)
Grass was created after 14161 combinations (Moss + Earth)
Reed was created after 14165 combinations (Grass + Swamp)
Piesiosauria was created after 14609 combinations (Water + Dinosaur)
1UP was created after 15595 combinations (Life + Mushroom)
Sick was created after 15967 combinations (Flu + Man)
Cochineal was created after 16358 combinations (Cactus + Beetle)
Hen Coop was created after 16467 combinations (Chicken + Hut)
Hourglass was created after 16474 combinations (Sand + Glass)
Brick House was created after 17019 combinations (Concrete + Brick)
Vulture was created after 17206 combinations (Bird + Corpse)
Undead was created after 17301 combinations (Zombie + Corpse)
Mold was created after 17805 combinations (Mushroom + Mud)
Mario was created after 17916 combinations (Man + 1UP)
Lava Lamp was created after 18066 combinations (Lamp + Lava)
Sugar was created after 18472 combinations (Lime + Reed)
Uncut diamond was created after 19740 combinations (Pressure + Coal)
Caramel was created after 19868 combinations (Sugar + Fire)
Carmine was created after 20643 combinations (Fire + Cochineal)
Time was created after 20749 combinations (Hourglass + Life)
Pig was created after 20835 combinations (Livestock + Mud)
Milk was created after 20849 combinations (Livestock + Man)
Frankenstein was created after 20904 combinations (Electricity + Corpse)
Hospital was created after 23027 combinations (Sick + Brick House)
Coca-Cola was created after 23212 combinations (Soda water + Carmine)
Tobacco was created after 23578 combinations (Fire + Grass)
Ashtray was created after 23800 combinations (Glass + Ash)
Genie was created after 24563 combinations (Ghost + Lamp)
Dam was created after 24890 combinations (Water + Brick)
Fat was created after 24924 combinations (Man + Pig)
Sex was created after 25563 combinations (Man + Man)
Beaver was created after 26066 combinations (Dam + Beast)
Manure was created after 27015 combinations (Livestock + Grass)
Fern was created after 27919 combinations (Swamp + Moss)
Smoke was created after 28705 combinations (Tobacco + Fire)
Bitumen was created after 29191 combinations (Kerogen + Pressure)
Bacon was created after 30820 combinations (Pig + Fire)
Ozone was created after 31391 combinations (Oxygen + Electricity)
Skyscraper was created after 31716 combinations (Brick House + Glass)
Petroleum was created after 33497 combinations (Bitumen + Pressure)
Soap was created after 34069 combinations (Ash + Fat)
Museum was created after 36120 combinations (Brick House + Fossil)
Light bulb was created after 37008 combinations (Electricity + Glass)
Farmer was created after 39100 combinations (Man + Seed)
Zoo was created after 40742 combinations (Beast + Museum)
Saltpeter was created after 41269 combinations (Limestone + Manure)
Scarab was created after 42238 combinations (Beetle + Manure)
Yogurt was created after 43270 combinations (Milk + Bacteria)
Gasoline was created after 44407 combinations (Petroleum + Pressure)
Combustion Engine was created after 44986 combinations (Steam engine + Gasoline)
Christmas Tree was created after 44997 combinations (Light bulb + Tree)
Grave was created after 46594 combinations (Earth + Corpse)
Light was created after 47772 combinations (Light bulb + Electricity)
City was created after 48742 combinations (Skyscraper + Skyscraper)
Yoshi was created after 49102 combinations (1UP + Egg)
Explosion was created after 51352 combinations (Fire + Gasoline)
Swine flu was created after 53031 combinations (Pig + Flu)
Firefly was created after 63480 combinations (Light + Beetle)
Soured milk was created after 65934 combinations (Yogurt + Milk)
Idea was created after 66523 combinations (Light bulb + Man)
Cemetery was created after 73850 combinations (Grave + Grave)
Lighthouse was created after 88977 combinations (Skyscraper + Light)
Quark was created after 97212 combinations (Fire + Soured milk)
Whey was created after 97212 combinations (Fire + Soured milk)
Fruit was created after 99107 combinations (Tree + Farmer)
Tool was created after 101336 combinations (Man + Metal)
Paper was created after 104233 combinations (Reed + Tool)
Diamond was created after 104356 combinations (Uncut diamond + Tool)
Wood was created after 106189 combinations (Tool + Tree)
Diet was created after 106910 combinations (Yogurt + Man)
Cigarettes was created after 107028 combinations (Tobacco + Paper)
Boat was created after 107392 combinations (Water + Wood)
Wooden ship was created after 109902 combinations (Wood + Boat)
Sailor was created after 113387 combinations (Man + Boat)
Poison was created after 114309 combinations (Tool + Mushroom)
Steamer was created after 115465 combinations (Wooden ship + Steam engine)
Coffin was created after 117106 combinations (Wood + Corpse)
Berry was created after 121925 combinations (Grass + Fruit)
Arable was created after 126093 combinations (Earth + Tool)
Grape was created after 129556 combinations (Wood + Earth)
Arms was created after 129746 combinations (Metal + Tool)
Wheel was created after 130009 combinations (Wood + Tool)
Bicycle was created after 130728 combinations (Wheel + Wheel)
Lightsaber was created after 131360 combinations (Arms + Light)
Motorcycle was created after 131564 combinations (Combustion Engine + Bicycle)
Wine was created after 143439 combinations (Grape + Alcohol)
Champagne was created after 144310 combinations (Soda water + Wine)
Poisoned Weapons was created after 144375 combinations (Arms + Poison)
Cart was created after 150962 combinations (Wood + Wheel)
Cheese was created after 152203 combinations (Fire + Quark)
Firearms was created after 153021 combinations (Gunpowder + Arms)
Hunter was created after 153132 combinations (Arms + Man)
Blood was created after 153311 combinations (Beast + Hunter)
Meat was created after 153311 combinations (Beast + Hunter)
Wool was created after 153311 combinations (Beast + Hunter)
Soldier was created after 153639 combinations (Firearms + Man)
Barbecue was created after 157499 combinations (Fire + Meat)
Feather was created after 159354 combinations (Hunter + Bird)
Team was created after 161198 combinations (Cart + Beast)
Car was created after 162663 combinations (Combustion Engine + Cart)
Knife was created after 164259 combinations (Tool + Meat)
Cloth was created after 164509 combinations (Tool + Wool)
Assassin was created after 166784 combinations (Poisoned Weapons + Man)
Stake was created after 167205 combinations (Wood + Knife)
Fondue was created after 167656 combinations (Cheese + Fire)
Prisoner was created after 168372 combinations (Time + Assassin)
Sniper was created after 170347 combinations (Firearms + Assassin)
Scissors was created after 170577 combinations (Knife + Knife)
Sailing ship was created after 171462 combinations (Wooden ship + Cloth)
VW beetle was created after 173046 combinations (Beetle + Car)
Book was created after 180323 combinations (Paper + Feather)
Library was created after 183947 combinations (Book + Book)
Wheat was created after 188408 combinations (Arable + Seed)
Spinning wheel was created after 190350 combinations (Wheel + Wool)
Clothing was created after 191118 combinations (Man + Cloth)
Yarn was created after 191196 combinations (Wool + Spinning wheel)
Fisherman was created after 191424 combinations (Hunter + Fish)
Locomotive was created after 191862 combinations (Cart + Steam engine)
Pinocchio was created after 195283 combinations (Wood + Life)
Beer was created after 196045 combinations (Alcohol + Wheat)
Leech was created after 199517 combinations (Worm + Blood)
Bar was created after 201504 combinations (Beer + Brick House)
Sweater was created after 208867 combinations (Yarn + Tool)
Motorboat was created after 209071 combinations (Boat + Combustion Engine)
Scientist was created after 210146 combinations (Library + Man)
Kama Sutra was created after 211334 combinations (Book + Sex)
Sailboat was created after 217201 combinations (Boat + Cloth)
Penicillin was created after 218469 combinations (Mold + Scientist)
Pillow was created after 218889 combinations (Feather + Cloth)
Flour was created after 230476 combinations (Stone + Wheat)
Vampire was created after 242230 combinations (Man + Blood)
Warrior was created after 246224 combinations (Hunter + Arms)
Chariot was created after 247333 combinations (Cart + Warrior)
Weevil was created after 247881 combinations (Flour + Beetle)
Dough was created after 250634 combinations (Water + Flour)
Bread was created after 250704 combinations (Dough + Fire)
Sandwich was created after 260090 combinations (Meat + Bread)
Bat was created after 264573 combinations (Bird + Vampire)
Pizza was created after 266164 combinations (Dough + Cheese)
Hero was created after 267710 combinations (Dragon + Warrior)
McDonald's was created after 268384 combinations (Coca-Cola + Sandwich)
Firefighter was created after 271828 combinations (Fire + Hero)
Sun was created after 274703 combinations (Sky + Chariot)
Obesity was created after 278233 combinations (Man + McDonald's)
Star was created after 282363 combinations (Sun + Scientist)
Werewolf was created after 323754 combinations (Beast + Vampire)
Twilight saga was created after 327577 combinations (Werewolf + Vampire)
Batman was created after 350552 combinations (Bat + Man)
Toast was created after 362405 combinations (Fire + Bread)
After 1000000 simulated random combinations, 
266 new elements were created out of the total possible 266.

Java Source Code for Simulation

Element.java class with method for combining two elements

package dmalchemy;

import java.util.LinkedList;

/**
 * This is the element class that is used for creating and combining elements.
 * The two fields of instance data are the name of the element and a boolean
 * variable called "terminalElement" which is true if the element cannot be combined
 * with anything else, false otherwise.
 * @author John Herold
 */
public class Element
{
    private String name;
    private boolean terminalElement;

    public Element(String newElementName, boolean isTerminal)
    {
        name = newElementName;
        terminalElement = isTerminal;
    }

    public String getName()
    {
        return name;
    }

    public boolean isTerminal()
    {
        return terminalElement;
    }

    // Takes another element and an array of strings containing the recipies for elements as paramters
    public LinkedList<Element> combineWith(Element otherElement, String recipeList[])
    {
        String currentRecipe[];
        LinkedList<Element> newElements = new LinkedList<Element>();
        for(int i = 0; i < recipeList.length; i++)
        {
            currentRecipe = recipeList[i].split("[+=]");
            if( (currentRecipe[1].trim().equalsIgnoreCase(name) && currentRecipe[2].trim().equalsIgnoreCase(otherElement.getName())) || (currentRecipe[2].trim().equalsIgnoreCase(name) && currentRecipe[1].trim().equalsIgnoreCase(otherElement.getName())) )
            {
                // There is a recipe for these two elements, this is a valid combination
                String newElementName = currentRecipe[0];
                boolean isTerminal = false;
                // Check if the element is terminal (denoted by an asterisk in the name)
                if(newElementName.contains("*"))
                {
                    isTerminal = true;
                    newElementName = newElementName.replace("*", "");
                }
                Element newElement = new Element(newElementName, isTerminal); // Create the new element
                newElements.add(newElement);
            }
        }
        return newElements; // return the linked list of new elements created (if any) in this combination
    }

}

CombinationSimulator.java with main():

package dmalchemy;

import java.io.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.util.ArrayList;
import java.util.LinkedList;
import java.util.Random;

/**
 * This is a simulation for combining random elements over time to see what happens
 * and what elements arise. It works by randomly combining two currently created elements
 * every iteration of the main loop and adding any new elements created to the list.
 * @author John Herold
 */
public class CombinationSimulator
{
    public static final File RECIPE_FILE = new File("combinations.txt");
    public static final int NUMBER_OF_SIMULATED_COMBINATIONS = 100000;

    public static void main(String[] Args)
    {
        String recipeList[] = null;
        ArrayList<Element> createdElements = new ArrayList<Element>();
        // Add starting elements to createdElements list
        createdElements.add(new Element("Earth", false));
        createdElements.add(new Element("Water", false));
        createdElements.add(new Element("Fire", false));
        createdElements.add(new Element("Air", false));
        // Load recipies from file
        try
        {
            BufferedReader fileReader = new BufferedReader(new FileReader(RECIPE_FILE));
            String nextLineInFile;
            int numberOfRecipies = 0;
            while((nextLineInFile = fileReader.readLine()) != null)
            {
                numberOfRecipies++;
            }
            fileReader.close();
            recipeList = new String[numberOfRecipies];
            fileReader = new BufferedReader(new FileReader(RECIPE_FILE));
            for(int i = 0; (nextLineInFile = fileReader.readLine()) != null; i++)
            {
                recipeList[i] = nextLineInFile;
            }
            fileReader.close();
        }
        catch(Exception e)
        {
            System.out.println("Error Loading From File " + RECIPE_FILE.getPath());
        }

        // Run the simulation
        Random rGenerator = new Random();
        for(int i = 1; i <= NUMBER_OF_SIMULATED_COMBINATIONS; i++)
        {
            int randomElement1 = rGenerator.nextInt(createdElements.size());
            int randomElement2 = rGenerator.nextInt(createdElements.size());
            Element element1 = createdElements.get(randomElement1);
            Element element2 = createdElements.get(randomElement2);
            //System.out.print("combining: " + element1.getName());
            //System.out.print(" and " + element2.getName() + "\n");
            if(!element1.isTerminal() && !element2.isTerminal()) // Make sure the elements aren't terminal and can be combined
            {
                // Try to combine them
                LinkedList<Element> combinations = element1.combineWith(element2, recipeList);

                // Traverse the returned linked list and add any new elements to the created list that aren't already in there
                for(int j = 0; j < combinations.size(); j++)
                {
                    boolean alreadyExists = false;
                    for(int k = 0; k < createdElements.size() && !alreadyExists; k++)
                    {
                        if(combinations.get(j).getName().equals(createdElements.get(k).getName()))
                            alreadyExists = true;
                    }
                    if(!alreadyExists)
                    {
                        createdElements.add(combinations.get(j));
                        System.out.println(combinations.get(j).getName() + " was created after " + i + " combinations (" + element1.getName() + " + " + element2.getName() + ")");
                    }
                }
            }
        }
        System.out.println("After " + NUMBER_OF_SIMULATED_COMBINATIONS + " simulated random combinations, " + (createdElements.size()-4) + " new elements were created out of the total possible " + recipeList.length + ".");
    }
}

The combinations.txt file I made for the program runs: (note the combination ideas aren't mine they are the from the original game, I just formatted them in a .txt file so I could parse them for my program)

1UP= life + mushroom 
Airplane*= metal + bird 
Alcohol= fire + water 
Alcoholic= man + alcohol
Algae= life + water 
Arable= earth + tool 
Arms= metal + tool 
Ash= fire + tree
Ashtray*= ash + glass 
Assassin= man + poisoned weapons 
Avian Flu*= flu + bird 
Bacon*= fire + pig 
Bacteria= life + swamp 
Bar*= brick house + beer 
Barbecue= fire + meat 
Bat= bird + vampire 
Batman*= man + bat 
Beach*= water + sand 
Bear*= beast + forest 
Beast= earth + lizard 
Beaver= dam + beast 
Beer= alcohol + wheat 
Beetle= earth + worm 
Berry= grass + fruit 
Bicycle= wheel + wheel 
Bird= air + egg 
Bitumen= pressure + kerogen
Blood= beast + hunter 
Boat= water + wood 
Boiler= metal + steam 
Book= feather + paper 
Bread= dough + fire 
Brick= clay + fire 
Brick House= brick + concrete 
Butterfly= air + worm 
Cactus= desert + tree 
Car= cart + combustion engine 
Caramel*= sugar + fire 
Carbon Dioxide= oxygen + man 
Carmine= cochineal + fire 
Cart= wheel + wood 
Caviar= fish + fish 
Cement= clay + limestone 
Cemetery*= grave + grave 
Ceramics*= clay + man 
Champagne*= wine + soda water 
Chariot= warrior + cart 
Cheese= quark + fire 
Chicken= egg + life 
Christmas Tree*= tree + light bulb 
Cigarettes= paper + tobacco 
City= skyscraper + skyscraper 
Clay= sand + swamp 
Cloth= tool + wool 
Clothing= cloth + man 
Cloud= air + steam 
Coal= fire + tree 
Coca-Cola= soda water + carmine 
Cochineal= cactus + beetle 
Coffin= corpse + wood 
Combustion Engine= steam engine + gasoline 
Concrete= cement + water 
Corpse= fire + man 
Dam= brick + water 
Desert= sand + sand 
Diamond*= uncut diamond + tool 
Diet= man + yogurt 
Dinosaur= earth + egg 
Dough= flour + water 
Dragon= fire + flying dinosaur 
Dust= air + earth 
Ectoplasm*= ghost + energy 
Egg= life + stone 
Electric eel*= snake + electricity 
Electric ray*= fish + electricity 
Electricity= energy + metal 
Energy= air + fire 
Explosion*= gasoline + fire 
Farmer= man + seed 
Fat= man + pig 
Feather= bird + hunter 
Fern= moss + swamp 
Fire Elemental= fire + life 
Firearms= arms + gunpowder 
Firefighter*= hero + fire 
Firefly*= light + beetle 
Fish= bacteria + plankton 
Fisherman*= hunter + fish 
Flour= stone + wheat 
Flower= water + seed 
Flu= air + bacteria 
Flying Dinosaur= air + dinosaur 
Fondue*= cheese + fire 
Forest= grove + grove 
Fossil= dinosaur + earth 
Frankenstein*= corpse + electricity 
Frog*= lizard + swamp 
Fruit= tree + farmer 
Gasoline= petroleum + pressure 
Genie*= lamp + ghost 
Geyser= steam + earth 
Ghost= ash + life 
Glass= fire + sand 
Golem= clay + life 
Grape= earth + wood 
Grass= earth + moss 
Grave= earth + corpse 
Grove= tree + tree 
Gunpowder= dust + fire
Hen Coop= chicken + hut 
Hero= dragon + warrior 
Hospital*= brick house + sick 
Hourglass= glass + sand 
Hunter= arms + man 
Hut= man + stone 
Hydrogen= water + electricity 
Idea*= man + light bulb 
Iodine= algae + fire 
Kama Sutra= book + sex 
Kerogen= fossil + pressure
Knife= meat + tool 
Lamp= fire + glass 
Lava= earth + fire 
Lava Golem= lava + life 
Lava Lamp*= lava + lamp 
Leech*= blood + worm 
Library= book + book 
Lichen*= mushroom + algae 
Life= energy + swamp 
Light= electricity + light bulb 
Light bulb= electricity + glass 
Lighthouse*= skyscraper + light 
Lightning Rod*= thunderstorm + metal 
Lightsaber*= arms + light 
Lime= fire + limestone 
Limestone= shells + stone 
Livestock= beast + man 
Lizard= snake + worm 
Locomotive*= cart + steam engine 
Man= beast + life 
Manure= grass + livestock 
Mario*= 1UP + man 
McDonald's= Coca-Cola + sandwich 
Meat= beast + hunter 
Metal= fire + stone 
Metal Golem*= life + metal 
Milk= livestock + man 
Mite*= life + dust 
Mold= mushroom + mud 
Molotov Cocktail*= fire + alcohol 
Moss= swamp + algae 
Motorboat*= boat + combustion engine 
Motorcycle*= bicycle + combustion engine 
Mud= dust + water 
Museum= brick house + fossil
Mushroom= earth + algae
Obesity= man + mcdonald's 
Omelette*= egg + fire 
Oxygen= water + electricity 
Oxyhydrogen= oxygen + hydrogen 
Ozone= oxygen + electricity 
Panda*= tree + beast 
Paper= reed + tool 
Pearl*= sand + shells 
Peat= swamp + tree 
Penicillin= mold + scientist 
Petri Dish*= glass + bacteria 
Petroleum= bitumen + pressure 
Phoenix*= bird + fire 
Pig= livestock + mud
Pillow*= feather + cloth 
Pinocchio*= wood + life 
Pizza*= cheese + dough 
Plankton= bacteria + water 
Piesiosauria*= dinosaur + water 
Poison= mushroom + tool 
Poisoned Weapons= arms + poison 
Pressure= earth + earth 
Prisoner*= assassin + time 
Quark= soured milk + fire 
Quetzalcoatl*= snake + bird 
Reed= grass + swamp 
Rust*= water + metal 
Sailboat= boat + cloth 
Sailing ship= cloth + wooden ship 
Sailor*= boat + man 
Salamander*= fire + lizard 
Saltpeter= limestone + manure 
Sand= stone + water 
Sandstorm*= storm + sand 
Sandwich= meat + bread 
Scarab*= beetle + manure 
Scientist= library + man 
Scissors*= knife + knife 
Scorpion= beetle + sand 
Scotch whiskey*= alcohol + peat 
Seed= life + sand 
Sex= man + man 
Shells= plankton + stone 
Sick= man + flu 
Silicon*= pressure +sand 
Sky= air + cloud 
Skyscraper= brick house + glass 
Smoke*= fire + tobacco 
Snail*= shells + worm 
Snake= swamp + worm 
Sniper*= assassin + firearms 
Soap*= ash + fat 
Soda water= carbon dioxide + water 
Soldier*= firearms + man 
Soured milk= milk + yogurt 
Spinning wheel= wheel + wool 
Stake= wood + knife 
Star*= sun + scientist 
Steam= air + water 
Steam engine= boiler + coal 
Steamer*= steam engine + wooden ship 
Stone= air + lava 
Storm= air + energy 
Sugar= lime + reed 
Sulfur= bacteria + swamp 
Sun= sky + chariot 
Sushi*= fish + algae 
Swamp= earth + water 
Sweater*= yarn + tool 
Swine flu*= pig + flu 
Team*= beast + cart 
Tequila= alcohol + worm 
Thunderbird*= bird + storm 
Thunderstorm= storm + electricity 
Time= life + hourglass 
Toast*= fire + bread 
Tobacco= fire + grass 
Tool= man + metal 
Totora*= forest + ghost 
Tree= earth + seed 
Turtle= egg + sand 
Twilight saga*= vampire + werewolf 
Typhoon*= storm + water 
Uncut diamond= coal + pressure 
Undead*= zombie + corpse
Vampire= blood + man 
Vinegar*= alcohol + oxygen 
Vodka= alcohol + water 
Volcano= lava + pressure 
Vulture*= corpse + bird 
VW beetle*= car + beetle 
Walking tree= life + tree 
Warrior= arms + hunter 
Weevil*= flour + beetle 
Werewolf= beast + vampire 
Whale*= beast + water 
Wheat= arable + seed 
Wheel= tool + wood 
Whey= soured milk + fire 
Wind= air + air 
Wine= grape + alcohol 
Wood= tool + tree 
Wooden ship= boat + wood 
Wool= beast + hunter 
Worm= earth + plankton 
Yarn= spinning wheel + wool 
Yogurt= bacteria + milk 
Yoshi*= 1up + egg 
Zombie= fossil + life 
Zoo*= beast + museum 
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