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Recipe for the week of April 3 - 9

A 1d Stepping Stone Model & A Puzzle for Webaholics

Here we see a space-time picture of a one-dimensional nearest neighbor stepping stone model. Each horizontal slice represents the state of the system at a certain time. The initial state is at the top; subsequent iterates proceed downward. The synchronous update rule is for each cell to simply choose one of its two nearest neighbors at random and adopt the color there. The spreading that occurs as your eye moves down the image is one-dimensional clustering. Actually, all the pixels at the top are alternately colored with uniform random intensities of either red or blue but, due to the synchronous dynamics, colors interweave to produce a nice dithering effect reminiscent of tissue collage. The checkerboard effect also explains why the reduction for this recipe's thumbnail gif shows only shades of red.

While surfing the web a few weeks ago I discovered a very nice title graphic at the Turbo Pascal Programmer's Page:


This is clearly a space-time realization of some 1d CA rule, but with time running up to give the impression of botanical growth rather than liquid drip. As a challenge to your gray matter, see if you can figure out the update rule for that image, which you can download as


I asked the creator of TPPP for his source, but received no response. If anyone can supply a reference, kindly send me feedback via the link on my chef's page.

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