Okay. A random post on the /r/cellular_automata subreddit inspired me.
Let’s generate a cellular automata where each pixel updates based on a neural network given as input:
Let’s do it!
L-Systems are pretty awesome. With only a bare few rules, you can turn something like this:
LSystem.new("Barnsley Fern") do
start "+++X"
rule "X", "F+[[X]-X]-F[-FX]+X"
rule "F", "FF"
terminal "F" do forward end
terminal "[" do push end
terminal "]" do pop end
terminal "-" do rotate -25 end
terminal "+" do rotate +25 end
end
Into this:
Let’s make magic circles/runes!
Turn this:
rune do
scale 0.9 do
circle
polygon 7
star 14, 3
star 7, 2
children 7, scale: 1/8r, offset: 1 do |i|
circle
invert do
text (0x2641 + i).chr Encoding::UTF_8
end
end
end
scale 0.15 do
translate x: -2 do circle; moon 0.45 end
circle
translate x: 2 do circle; moon 0.55 end
end
end
Into this:
The fine people of /r/generative / Genuary2021 have a series of challenges for generative works for the month of January. I don’t think I’m going to do all of them, but pick and choose. For example, the very first prompt is:
// TRIPLE NESTED LOOP
My goal was to draw a grid of circles across the X/Y the image and nest them for the third dimension. To make it a little more interesting, I added a few different color modes. seededRandom is my personal favorite, that was interesting to get working.
Much like transpiling register machines, now we have a chance to transpile stack machines. Unfortunately, it doesn’t actually speed up the code nearly so much (the stack is just not as effective of a memory structure in this case), but it’s still an interesting bit of code.
In this case, we turn something like this:
invsub
polT
writeG
id
neg
zero?
sin
invsub
ZERO
inv
Into this:
function(X, Y) {
this.x = X;
this.y = Y;
this.stack = [];
this.r = undefined;
this.g = undefined;
this.b = undefined;
this.stack.push(X);
this.stack.push(Y);
var arg0 = 0;
var arg1 = 0;
var arg2 = 0;
var result = 0;
// invsub
arg0 = this.stack.pop() || 0;
result = 1 - arg0;
result = result % 1.0;
this.stack.push(result);
// polT
arg0 = this.stack.pop() || 0;
arg1 = this.stack.pop() || 0;
result = Math.atan2(arg0, arg1);
result = result % 1.0;
this.stack.push(result);
// writeG
arg0 = this.stack.pop() || 0;
this.g = arg0;
// id
arg0 = this.stack.pop() || 0;
result = arg0;
result = result % 1.0;
this.stack.push(result);
// neg
arg0 = this.stack.pop() || 0;
result = -arg0;
result = result % 1.0;
this.stack.push(result);
// zero?
arg0 = this.stack.pop() || 0;
arg1 = this.stack.pop() || 0;
arg2 = this.stack.pop() || 0;
result = arg0 === 0 ? arg1 : arg2;
result = result % 1.0;
this.stack.push(result);
// sin
arg0 = this.stack.pop() || 0;
result = Math.sin(arg0);
result = result % 1.0;
this.stack.push(result);
// invsub
arg0 = this.stack.pop() || 0;
result = 1 - arg0;
result = result % 1.0;
this.stack.push(result);
// ZERO
result = 0;
result = result % 1.0;
this.stack.push(result);
// inv
arg0 = this.stack.pop() || 0;
result = 1 / arg0;
result = result % 1.0;
this.stack.push(result);
return [
this.r === undefined ? this.stack.pop() || 0 : this.r,
this.g === undefined ? this.stack.pop() || 0 : this.g,
this.b === undefined ? this.stack.pop() || 0 : this.b,
];
}
Okay, enough with register machines. Let’s make something new. This time, a stack based machine!
Rather than keeping it’s memory in a series of memory cells, there will be a single stack of values. All functions can pop values from the top of the stack or push them back on. I will add the ability to read the X/Y value and directly write R/G/B, but you can’t write to the former or read from the latter, so you can’t use them as registers. Let’s see what that looks like!
Okay. That is slow… Let’s make it faster!
So the main problem we have is that we’re interpreting the code. For every single pixel, for every line of code, we’re doing a few housekeeping things and making at least one function call. For a 400x400 image with just 10 lines of code, that’s 1.6M function calls. Like I said, slow.
So let’s make it faster!
My first idea? Transpile it to Javascript!
Now that I’ve got register machines working, one of the next ideas I had was to implement different wrapping modes. Currently, as it stands, X and Y are passed into the machine as floating point numbers from [0, 1] across the image and output is expected to be [0, 1] for each of R, G, and B. Any values that end up outside of that range, we truncate down to that range. But some of our mathematical functions (multiplication, exponentiation, negation, etc) tend to generate numbers way out of this range. But they don’t have to!