Reversed formula Julia set, a fractal.

Formula used:

${\displaystyle z_{n+1}={\sqrt {z_{n}-c}}}$

${\displaystyle C=0.4,0.3i}$

One of the two roots are selected by random and then after a number of pre-iterations (10-20) the position of ${\displaystyle Z}$ is constantly plotted after each iteration. The method is very much like the "random game" IFS method.

See also:

• w:en:Julia set#Julia set using reversed formula
• w:sv:Juliamängden#Reverserad formel

Image: User:Solkoll. Public domainPublic domainfalsefalse This work has been released into the public domain by its author, Solkoll. This applies worldwide. In some countries this may not be legally possible; if so: Solkoll grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. More fractals from my tools: Image:Fractal dimension.jpg Image:Harter-Heighways dragon curve (IFS).jpg Image:Koch curve (L-system construction).jpg Image:Koch curve (IFS).jpg Image:Koch snowflake (RGB-CMY).jpg Image:Lévy's C-curve (IFS).jpg Image:Lévy's dragon curve (IFS).jpg Image:Mandelbrot inside (64 iters B&W).gif Image:Mandelbrot inside (64 iters colour).gif Image:Menger sponge (2D).jpg Image:Julia set (C = 0.285, 0.01).jpg Image:Julia set (C = 0.285, 0.01) II.jpg Image:Julia set (Detail 01).jpg Image:Julia set (Detail 02).jpg Image:Julia set (highres 01).jpg Image:Julia set (highres 02).jpg Image:Julia set (Rev formula 01).jpg Image:Julia set (Rev formula 02).jpg Image:Julia set (Rev formula 03).jpg Image:Julia set (Rev formula 04).gif Image:Reversed Julia set C = ( 0.4 0.3 ).gif Image:Sierpinski square.jpg Image:Sierpinski triangle (blue).jpg Image:Sierpinski triangle (RGB).jpg Image:Solkoch.jpg 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