Visualizing distributions with pepperoni pizza (and JavaScript) – nicole web

Summary

There's a pizza shop near me that serves a normal pizza. I mean, they distribute the toppings in a normal way. They're not uniform at all. The toppings are random, but not the way I want. The colloquial understanding of "random" is kind of the Platonic ideal of a pizza: slightly chaotic but things are more or less spread out over the whole piece in a regular way. If you take a slice you'll get more of less the same amount of pepperoni as any other slice. And every bite will have roughly the same amount of pepperoni as every other bite. I think it would look something like this. Regenerate this pie! This pizza to me is pretty much the canonical mental pizza. It looks pretty random, but you know what you're gonna get. And it is random! Here's how we made it, with the visualiztion part glossed over. First, we make a helper function, since Math.random() gives us values from 0 to 1, but we want values from -1 to 1. // return a uniform random value in [-1, 1) function randUniform() { return 2*Math.random() - 1; } Then, we make a simple function that gives us the coordinates of where to put a pepperoni piece, from the uniform distribution. function uniformPepperoniPosition() { var [centerX, centerY, radius] = pepperoniBounds(); let x = radius*2; let y = radius*2; while (x**2 + y**2 >= radius**2) { x = randUniform() * radius; y = randUniform() * radius; } return [x+centerX, y+centerY]; } And we cap it off with placing 300 fresh pieces of pepperoni on this pie, before we send it into the oven. (It's an outrageous amount of very small pepperoni, chosen in both axes for ease of visualizing the distribution rather than realism.) function drawUniformPizza() { drawBackground(); drawPizzaCrust(); drawCheese(); var [_, _, radius] = pepperoniBounds(); for (let p = 0; p < 300; p++) { let [x,y] = uniformPepperoniPosition(); drawPepperoni(x, y); } } But it's not what my local pizza shop's pizza's look like. That's because they're not using the same probability distribution. This pizza ...