This Python script generates visually striking patterns based on the algorithm known as Circle². The underlying mathematical idea was developed by John E. Connett, at the University of Minnesota. The method was later popularized and named "Circle²" by A.K. Dewdney in his Computer Recreations column in Scientific American (September 1986). The method explores the mathematical beauty of the equation:
By applying this formula across a grid of coordinates and assigning colors based on the result, it produces hypnotic, circular wallpaper designs.
At the heart of the pattern is the squared sum of coordinates:
Each point (x, y) on a grid is evaluated using this equation. The value of z is then either directly converted to an integer or used with a modulo operation to index into a color palette, creating cyclical, ring-like patterns.
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Grid Construction: A rectangular grid is defined using customizable corner and size parameters. In the optimized version, this grid is built using NumPy for speed and efficiency.
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Computation & Coloring:
zis computed at each grid point.- Colors are assigned by taking
int(z) % NUM_COLORS, cycling through a fixed palette. - The classic version used loops; the current version uses vectorized operations for faster rendering.
You can tweak these parameters to generate unique visual styles:
- WIDTH, HEIGHT: Image resolution.
- CORNER_A, CORNER_B: Coordinates of the lower-left corner of the grid.
- SIDE: Length of the square grid area.
- NUM_COLORS: Number of distinct colors in the palette