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Argggh, ItS a Julia, I'm sure.

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Experimenting with the op-art strip effect:

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A zoom on one of the spirals in:

https://plus.google.com/101799841244447089430/posts/HZyY9ZiFRUj

at point (-.871158, .08286), zoom radius of .0000098.

Strange!

#Fractal #Julia #Mandelbrot #Math

https://plus.google.com/101799841244447089430/posts/HZyY9ZiFRUj

at point (-.871158, .08286), zoom radius of .0000098.

Strange!

*___*#Fractal #Julia #Mandelbrot #Math

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A zoom on the top of at point (-.055, .97) at zoom radius .03:

https://plus.google.com/101799841244447089430/posts/E7AZLycvJh9

with a single change in the formula. The fractional power of 1.9 is now 2.

#Fractal #Julia #Space #Math

https://plus.google.com/101799841244447089430/posts/E7AZLycvJh9

with a single change in the formula. The fractional power of 1.9 is now 2.

*___________*#Fractal #Julia #Space #Math

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Finally a Siegel disk experiment that looks like a Siegel disk:( with a curvature monitor)

f[z_]=z^2-N[(3+I)/Sqrt[10]]*z

f[z_]=z^2-N[(3+I)/Sqrt[10]]*z

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Here is the new circle monitor on the same Julia:

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Same Siegel disk as ifs with field and circles monitors:

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Fwiw, here is what I get with one single change from the following code:

https://plus.google.com/101799841244447089430/posts/dMNBYdCYjYd

I mutated the mod conditional from:

if (! ((i + 1) % 4))

to:

if (((i + 1) % 4))

Wow, what a difference. Thanks again to +Owen Maresh for his try:

https://plus.google.com/+OwenMaresh/posts/9R6dvNWDK8m

on recreating the original here:

https://plus.google.com/101799841244447089430/posts/Grb2inEG79b

:^D

#Fractal #Julia #Mandelbrot #Space #Math

https://plus.google.com/101799841244447089430/posts/dMNBYdCYjYd

I mutated the mod conditional from:

if (! ((i + 1) % 4))

to:

if (((i + 1) % 4))

Wow, what a difference. Thanks again to +Owen Maresh for his try:

https://plus.google.com/+OwenMaresh/posts/9R6dvNWDK8m

on recreating the original here:

https://plus.google.com/101799841244447089430/posts/Grb2inEG79b

:^D

*___*#Fractal #Julia #Mandelbrot #Space #Math

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Another simplified Siegel disk experiment that gives a "budding" effect:

f[z_]=z^2-Exp[I*2*Pi/5]*z

f[z_]=z^2-Exp[I*2*Pi/5]*z

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+Chris Thomasson: I attempted to reimplement exactly what you had in mpmath, and I got somewhere else?

#!/usr/bin/python

from mpmath import *

import pylab

def rhai(z):

c = z

for u in range(1,100):

if (((u+ 1) % 4)!=0):

z = z*z +c

mul = im(z)+re(z)

if(mul==0.0):

mul = 0.000000001

z = z**2 + (re(z)+im(z))/mul * 0.01

if ((re(z)*re(z)+im(z)+im(z))>52):

break

return z/abs(z)

fp.cplot(lambda z: rhai(z), [-1.1,1.1], [-1.1,1.1], points=20000000, dpi=400, verbose=True, file="serenxhua.png")

#!/usr/bin/python

from mpmath import *

import pylab

def rhai(z):

c = z

for u in range(1,100):

if (((u+ 1) % 4)!=0):

z = z*z +c

mul = im(z)+re(z)

if(mul==0.0):

mul = 0.000000001

z = z**2 + (re(z)+im(z))/mul * 0.01

if ((re(z)*re(z)+im(z)+im(z))>52):

break

return z/abs(z)

fp.cplot(lambda z: rhai(z), [-1.1,1.1], [-1.1,1.1], points=20000000, dpi=400, verbose=True, file="serenxhua.png")

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