Hopalong Image Generator

an interactive Java applet

This Java applet generates a unique fractal image before your eyes, based on Martin's Hopalong algorithm

Instructions:

• Your browser requires Java in order to see the image.
• To see a random image, click on the New Image button.
• The shape of the image depends on the parameters a, b, and c. To change the parameters, type the values in the text boxes, then click on the Change a,b,c button.
• Change Color will toggle the background color between black and white.
• Zoom In and Zoom Out will magnify or shrink the image.

How it works:

These images are generated by repeatedly applying a mapping function discovered by Barry Martin, of Aston University in England. This mapping was described in an article by A.K. Dewdney in the September 1986 issue of Scientific American magazine. Dewdney calls it Hopalong, but Martin prefers the name Martin's Mapping. The set of points generated by the mapping is called the orbit. This is the formula:

x_{n + 1} = y_n - sign(x_n) * sqrt|b*x_n - c|

y_{n + 1} = a - x_n

Depending on the values of the parameters a, b, and c, the orbital will vary, and the image will look different. You can change the parameters and look for a pattern that you like best.

You can watch the image emerge from nothing and grow as the points appear one at a time in changing colors. Get the Java source code here.

Related web sites

• Another Java applet that generates Hopalong images, from Martin Junglas
• HOP is a program which lets you apply all kinds of special effects to Hopalong images.
• Fractint generates Hopalong images, and other fractals.
• Huepfer a page about Hopalong, in German.

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Pac Sun

David Imai, dimai at email.com

Modified 07-May-2004 09:06 PM