A procedurally generated chemistry

We can appropriately characterize chemistry as the interactions between basic elements. In the real world, elements are atoms. In Flat Galaxy, basic elements will be somewhat different. We're going to come up with a chemistry-creation scheme that contains enough randomness to give us something different every time but with enough structure that we can expect to be able to use some of the results.

Let's start by generating around 100 random numbers from 1-100:

89 31 64 4 60 ... 71 75 7 48 53

These are our elements. Think of them as atomic numbers (not atomic weights). We would expect to get each number about once on average, but in one trial we won't, and we're going to cut out duplicates. This leaves us with slightly fewer than our expected number (exactly how many is, I believe, a probabilistic "expected" function).

Now let's generate a semi-random "fixing" number in the lower half of our number range:

20

What is the point of this fixing number? It's entirely arbitrary, but it gives us a reference point from which we can tease out relationships between our elements. Why in the lower half of our number range? No reason, other than it'll give us interesting values. I actually picked 20 in this case because it's close to the number we would expect to get consistently with enough trials (remember, random number in the lower half of a range of numbers from 1 to slightly less than 100).

Now what? Well, from here we start examining similarities in the numbers based on breaking their values up into discrete chunks, kind of like how electrons in atoms are broken up into electron shells. The amount of "electrons" each shell can fit is determined by a function loosely based on the general 2n^2 value in real-life chemistry, where n is the shell number, but which also incorporates our fixing number from earlier. This gives us some interesting values for shell capacities, and I've even had it exactly mimic real life electron shell capacities on occasion.

Once our "elements" are given shells with capacities, we divide their "electrons" up into these shells and whatever is left over in the final shell is what that element has to make bonds with other elements. For example, if Element 30 has 12 electrons in its outermost shell which has a capacity of 20, we know that Element 30 will readily bond with any element looking to either give up 8 electrons (ie has 8 electrons in its outer shell) or any element looking to gain 12 electrons. From here, we can group our elements with similar bonding properties together, and even construct a "periodic table." Due to the randomness I've introduced into the system, this table ranges from narrow and deep to wide and shallow (based largely on the fixing number--larger fixing number means a wider, shallower table). It doesn't quite measure up to the real life periodic table, but there's a lot of subtlety it's still missing. Here are a couple examples, with similar elements in the same columns:

Number of elements targeted: 118
Number of elements actually generated: 101
Generated fix: 5
[ 1 ][ 3 ][ 4 ][ 5 ][ 10][ 11][ 12][ 13][ 14][ 15]
[ 2 ][ 7 ][ 8 ][ 9 ][ 25][ 26][ 27][ 38][ 39][ 30]
[ 16][ 17][ 18][ 19][ 35][ 36][ 47][ 48][ 49][ 40]
[ 20][ 22][ 33][ 24][ 45][ 46][ 57][ 58][ 59][ 50]
[ 31][ 32][ 43][ 34][ 55][ 56][ 67][ 68][ 69][ 60]
[ 41][ 42][ 53][ 44][ 65][ 66][ 77][ 78][ 99][ 80]
[ 51][ 52][ 73][ 54][ 75][ 76][ 87][108][109][ 90]
[ 61][ 72][ 83][ 64][ 85][ 86][ 97][118][   ][100]
[ 71][ 82][103][ 74][ 95][ 96][107][   ][   ][   ]
[ 81][ 92][113][ 84][105][106][117][   ][   ][   ]
[ 91][102][   ][ 94][115][116][   ][   ][   ][   ]
[101][112][   ][114][   ][   ][   ][   ][   ][   ]

Sorry about the font size and spacing here. It was necessary to make it fit.

Number of elements targeted: 118
Number of elements actually generated: 121
Generated fix: 12

[ 2 ][ 9 ][ 4 ][ 5 ][ 6 ][ 7 ][ 14][ 15][ 16][ 56][ 18][ 19][ 20][ 21][ 22][ 39][ 38][ 41][ 40][ 43][ 42][ 45][ 90][ 46]
[ 23][ 24][ 10][ 11][ 12][ 28][ 29][ 54][ 31][ 78][ 33][ 34][ 35][ 36][ 37][ 85][108][ 87][ 86][ 89][ 88][ 91][114][ 92]
[ 47][ 48][ 25][ 26][ 27][ 52][ 53][ 76][ 55][102][ 57][ 58][ 59][ 82][ 61][109][132][111][110][113][112][115][   ][116]
[ 62][ 63][ 49][ 50][ 51][ 67][ 75][100][ 77][126][ 79][ 80][ 81][130][ 83][133][   ][135][134][   ][   ][   ][   ][   ]
[ 68][ 70][ 64][ 65][ 66][ 74][   ][124][101][   ][103][104][105][   ][107][   ][   ][   ][   ][   ][   ][   ][   ][   ]
[ 69][ 94][ 71][ 72][ 73][ 98][   ][   ][125][   ][127][128][   ][   ][131][   ][   ][   ][   ][   ][   ][   ][   ][   ]
[ 93][118][ 95][ 96][ 97][122][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ]
[117][   ][119][120][121][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ]

You can definitely see some patterns in the numbers which I'd like to mix up a bit, and it's not exactly scientific, but it's a start.