Title: Mandelbrot Spokes and Spirals Post by: element90 on July 14, 2013, 01:54:08 PM (https://copy.com/jUS84N3mHd2z)
https://copy.com/jUS84N3mHd2z (https://copy.com/jUS84N3mHd2z) Modified Mandelbrot: Complex plane transformation: circle fold out (diameter 1.5) tanh Transform set A asin Transform set B add -0.5 Transform sequence: BAA Formula: z = transform(z) z = z*z + c Transform B is applied to iterations 1, 4, 7 ... etc, transform 2, 3, 5, 6, 8, 9 ... etc. Title: Re: Mandelbrot Spokes and Spirals Post by: cKleinhuis on July 14, 2013, 03:14:10 PM nice pic, a standard mset?
Title: Re: Mandelbrot Spokes and Spirals Post by: element90 on July 14, 2013, 03:50:50 PM The basic formula is the Standard Mandelbrot set, however, the complex plane has be transformed and two transform sets are periodically applied to z before evaluating z*z + c, one set is applied twice as often as the other.
The modifications are detailed below the picture. I'm preparing some pictures to show roughly where the picture is located and how the fractal looks a a whole. Title: Re: Mandelbrot Spokes and Spirals Post by: element90 on July 14, 2013, 05:43:58 PM The initial picture is from a location somewhere on the left hand side of the trench in the following picture which looks pretty much like the Standard Mandelbrot set. (https://copy.com/G2iRNThKKer0) https://copy.com/G2iRNThKKer0 (https://copy.com/G2iRNThKKer0) It isn't the standard Mandelbrot set, zooming out ... (https://copy.com/3mCRZy49gjgV) https://copy.com/3mCRZy49gjgV (https://copy.com/3mCRZy49gjgV) And zooming out again ... (https://copy.com/E3PC2ExQW22K) https://copy.com/E3PC2ExQW22K (https://copy.com/E3PC2ExQW22K) The picture above shows copies above and below, there are more copies above which get bigger and more copies below which get smaller. Zooming out again ... (https://copy.com/7AdD6aYFRjHP) https://copy.com/7AdD6aYFRjHP (https://copy.com/7AdD6aYFRjHP) and again ... (https://copy.com/98pkiJwkydIy) https://copy.com/98pkiJwkydIy (https://copy.com/98pkiJwkydIy) The mutant Mandelbrots above and below repeat indefinitely. |