The so called "Pop Corn"" images where created by Cliff Pickover quite some time ago. The idea behind them is to plot the evolution of a dynamical system like
p'(t) = v(p)
where p is a point and v is a stationary velocity field. To make such simulation in a computer, the simplest way is to code some simple Euler
integrator which will simulate the derivative with some differences and a small delta time. In two dimensions, that would look like this:
xn+1 = xn + λ·f(x,y)
yn+1 = yn + λ·g(x,y)
where λ is the time step value (it should be something small). Now it's up to you to choose nice formulas for f(p) and g(p).
The original Pickover's formulas were trigonometric functions, but you can input anything you like. In my experiments of 1999 I used the original Pickover's formulas. The
result made it into the 64 kb demo called rare.
Later in 2006 I made this video where I animated f(p) and g(p) over time. Again, I used
trigonometric functions (similar to Pickover's too) cause they produce some nice fluid-like shapes. The video is split in four different parts, with one different formula each.
As an example, this is the formula used for the second one>:
f(x,y) = cos( t0 + y + cos(t1+ πx))
g(x,y) = cos( t2 + x + cos(t3+ πy))
The ti parameters are linearly time varying values that produce the actual animation.
Below this text you can see some of the frames of the video (click to enlarge):