Hopalong is an "orbit" type fractal like lorenz. The image is obtained by iterating this formula after setting z(0) = y(0) = 0:
x(n+1) = y(n) - sign(x(n))*sqrt(abs(b*x(n)-c)) y(n+1) = a - x(n)Parameters are a, b, and c. The function "sign()" returns 1 if the argument is positive, -1 if argument is negative.
This fractal continues to develop in surprising ways after many iterations.
Another Martin fractal is simpler. The iterated formula is:
x(n+1) = y(n) - sin(x(n)) y(n+1) = a - x(n)
The parameter is "a". Try values near the number pi.
Michael Peters has based the HOP program on variations of these Martin types. You will find three of these here: chip, quadruptwo, and threeply.