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Carotid-Kundalini Fractal

CarotidKundaliniFractal

A fractal-like structure is produced for x<0 by superposing plots of Carotid-Kundalini functions ck_n of different orders n. the region -1<x<0 is called fractal land by Pickover (1995), the central region the Gaussian mountain range, and the region 0<x<1 oscillation land. The plot above shows n=1 to 25. Gaps in fractal land occur whenever

xcos^(-1)x=2pip/q

for p and q relatively prime integers. At such points x, the functions assume the [(q+1)/2] values cos(2pir/q) for r=0, 1, ..., |_q/2_|, where [z] is the ceiling function and |_z_| is the floor function.

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References

Pickover, C. A. "Are Infinite Carotid-Kundalini Functions Fractal?" Ch. 24 in Keys to Infinity. New York: Wiley, pp. 179-181, 1995.

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Carotid-Kundalini Fractal

Cite this as:

Weisstein, Eric W. "Carotid-Kundalini Fractal." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Carotid-KundaliniFractal.html

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