Mandelbrot Spokes and Spirals

[element90]

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.

[cKleinhuis]

nice pic, a standard mset?

[element90]

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.

[element90]

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

It isn't the standard Mandelbrot set, zooming out ...


https://copy.com/3mCRZy49gjgV

And zooming out again ...


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

and again ...


https://copy.com/98pkiJwkydIy

The mutant Mandelbrots above and below repeat indefinitely.