Dr. Dewdney credited Dr. Barry Martin, then a mathematics professor at Aston University, Birmingham, United Kingdom for the attractor. Dewdney named the attractor Hopalong because it hops from point to point.
Martin's algorithm takes a single seed value and iterates it to produce a wide variety of interesting images.
The equations are:
x = y – SGN(x) * √(ABS(b*x – c))
y = a – xThis series of (x, y) coordinates is specified by an initial point (xo, yo) and three constants a, b, and c.
The following is an example taken from the Scratch program where a = 0.4, b = 1, and c = 0 and the magnification set at 100. The initial point is (0, 0), the origin.
The Scratch project can be viewed and downloaded at the following link.
If you would like a description of the Scratch code and a Gallery of Hopalong images just send an email request to