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Described here is a pattern which grows fonts or words or fractal shapes by random walk techniques as described in the next TOPSY-TURVY pattern. This pattern however shows that the seeded points do not have to be regular geometric figures. To generate this pattern, the word “fractals“ was written using a drawing package. For effect, the word was also underscored with a wiggly line. The word “fractals” and its underscore were then used as seeded points. Each random walk was started by choosing a column (0, 1,…, 639) and a row (0, 1,…, 479) at random. The search would then begin in any one of the four major directions, the distance of one pixel at a time, looking for seeded points. When a seeded point was found the searching pixel stuck to it and another starting point was generated and the search repeated. To prevent overcrowding as more and more pixels aggregated on the screen, the program only allowed a starting point to occur if it was more than 9 pixels away from any other pixel on the screen. If overcrowding was detected, a new potential starting was generated. Using this overcrowding protection prevents the random starting points from occurring too close to the points which are already aggregated. This helps to maintain the fractal quality of the pattern. Without the overcrowding DENSITY function in the program, the growth could have lumpy and solid spots. Seeded points can be made with different colors and an ABSORB color function can cause searching pixels to take on the color of the seeded pixel. Thus, clusters of different colors may be grown on the screen. With seeded pixels broadly outlining anything from fonts to countries, interesting patterns emerge…

Described here is a pattern which was grown using a program developed by the author. The program generates fractal shapes by random walks of “sticky“ diffusing particles as described by Pickover [2].

In this Topsy-Turvy growth, a rectangle is drawn along the perimeter of the screen using conventional graphics and constitutes the seeded points. The starting point for the search starts anywhere on the screen as if it were dropped from the third dimension. To prevent overcrowding, a DENSITY function is used which rejects a starting point if it is within a certain distance, e.g., 9 pixels, of any pixel already on the screen…