Pickover Stalk

biomorphs

Pickover stalks are certain kinds of details to be found empirically in the Mandelbrot set, in the study of fractal geometry. They are so named after the researcher Clifford Pickover, whose ‘epsilon cross’ method was instrumental in their discovery. An ‘epsilon cross’ is a cross-shaped orbit trap, which is a method of coloring fractal images based upon how close an iterative function, used to create the fractal, approaches a geometric shape, called a ‘trap.’ Pickover hit on the novel concept of looking to see how closely the orbits of interior points come to the x and y axes. In these pictures, the closer that the point approaches, the higher up the color scale, with red denoting the closest approach. The logarithm of the distance is taken to accentuate the details.

Biomorphs are biological-looking Pickover Stalks. At the end of the 1980s, Pickover developed biological feedback organisms similar to Julia sets and the fractal Mandelbrot set. He described an algorithm which could be used for the creation of diverse and complicated forms resembling invertebrate organisms. The shapes are complicated and difficult to predict before actually experimenting with the mappings. He hoped these techniques would encourage others to explore further and discover new forms, by accident, that are on the edge of science and art. Pickover’s biomorphs show a self-similarity at different scales and illustrate a significant feature of feedback in dynamical systems. Real systems, such as human beings and mountain ranges, also show self-similarity at different scales.

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