MAKE A MEME
View Large Image
| View Original: | Mandel-bifurk.jpg (802x402) | |||
| Download: | Original | Medium | Small | Thumb |
| Courtesy of: | commons.wikimedia.org | More Like This | ||
| Keywords: Mandel-bifurk.jpg Comparsion of the functions of the Mandelbrot set and a bifurcation diagram The function for the Mandelbrot-set is Z<sub>n+1</sub> Z<sub>n</sub><sup>2</sup> + C The function for the standard bifucation-diagram is X<sub>n+1</sub> A · X<sub>n</sub> · 1 - X<sub>n</sub> 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 X<sub>n+1</sub> X<sub>n</sub><sup>2</sup> + A And the complex bifurcation function is Z<sub>n+1</sub> C · Z<sub>n</sub> · 1 - Z<sub>n</sub> 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 Solkoll 2D Mandelbrot set properties badjpg | ||||
