File:Mandel-bifurk.jpg
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Captions
Comparsion of the functions of the Mandelbrot set and a bifurcation diagram.
The function for the Mandelbrot-set is:
- Zn+1 = Zn2 + C
The function for the (standard) bifucation-diagram is:
- Xn+1 = A · Xn · (1 - Xn)
The Mandel-formula is using a complex-number format, the bifurcation is using real numbers. But the formulas can be altered to the diffrent form and used to write the Mandel as a bifurcation and the bifurcation as a complex escape-time fractal.
The real number Mandel formula is:
- Xn+1 = Xn2 + A
And the complex bifurcation function is:
- Zn+1 = C · Zn · (1 - Zn)
The image above shows all four variations, to the left the Mandelbort formula as a bifurcation diagram in white and also the complex "escape-time" visulation of the complex formula in blue, to the right, the same for the (standar, there are a lot of those =) bifurcation formula and as we can see, these formulas are strongly related.
Image: User:Solkoll.
All fractals are from self-written tools - linear IFS images from my: "2D IFS Studio", non-linear (rev Julia) from "3D RJIFS", (that also writes 2D rev Julias), escape time Z² fractals from "Julia dream", the rest are from small "hacks". See also: Solkoll & Solkoll 3D
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current | 10:09, 30 May 2005 | 802 × 402 (82 KB) | Solkoll~commonswiki (talk | contribs) | Comparsion of the functions for the Mandelbrot set and a Bifurcation diagram. {{Solkoll 2D}} |
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