The designs I call MindFlowers are specially constructed using multi-dimensional functions in polar co-ordinates. The process of construction can be visualized as a moving band which varies in position, color, and width in a symmetrical pattern around a common center. Each locus of the band might be designated B, where B = (p, d, c) where p is the position of the center of the band, d is its diameter, and c is its color. p, of course, is a two-dimensional point in polar co-ordinates, (r,
O). In effect we have four variables, r, O, d, and c, of which c is a three-dimensional color vector, (red, green, blue). Each of the four variables is a function of a single parameter t which can be thought of as an iteration of time. Thus we would have r = f1(t), O = f2(t), and so on.
The difficulty lies in designing the functions; the process requires a lot of trial and error. As an example, MindFlower #1 has r = 0.03 (sin(4(Pi)t) + 1) and
O = 0.3 + 0.34 (Sin(2(Pi)t) + 1).
Each design is then repeated at certain intervals in a radial symmetry, to make a design with identical radial parts.
Last Updated June 9th, 2002
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