• August 02, 2021, 08:16:06 AM

### Author Topic:  The Multi-Julia...  (Read 361 times)

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#### Chris_M_Thomasson

• Fractal Feline
• Posts: 154
• Programmer by trade; love fractals and math! :^)
##### The Multi-Julia...
« on: May 27, 2021, 10:55:31 AM »
This is a technique I came up with a while back that uses multiple Julia sets during reverse iteration. The n-ary roots of the complex numbers are chosen using a probability factor. Also, the Julia sets are chosen using another probability factor during iteration. Actually, a friend of mine actually wrote a little page about my work. Here it is:

http://paulbourke.net/fractals/multijulia/

It's a Fractal Life, 247... ;^)

#### Chris_M_Thomasson

• Fractal Feline
• Posts: 154
• Programmer by trade; love fractals and math! :^)
##### Re: The Multi-Julia...
« Reply #1 on: July 19, 2021, 05:47:32 AM »
Here is a fairly decent spiral formation created from two Julia sets:

ct_complex jp_sets[2] = { { -1, 1 }, { 1, -1} }; // spiral

I plotted one of my vector fields over some of its IFS points as well.

#### Chris_M_Thomasson

• Fractal Feline
• Posts: 154
• Programmer by trade; love fractals and math! :^)
##### Re: The Multi-Julia...
« Reply #2 on: July 19, 2021, 06:19:21 AM »
A zoom on the dead center, origin at (0, 0):

#### Chris_M_Thomasson

• Fractal Feline
• Posts: 154
• Programmer by trade; love fractals and math! :^)
##### Re: The Multi-Julia...
« Reply #3 on: July 19, 2021, 10:03:19 PM »
42 lines, and a six lines per vector field source:

#### lkmitch

• Fractal Phenom
• Posts: 51
##### Re: The Multi-Julia...
« Reply #4 on: July 21, 2021, 12:22:01 AM »
Here are two attempts. The circular one uses 8 different parameter values, from the 1/9, 2/9, ..., 7/9, and 8/9 disk tangent points to the main cardioid. The other uses (-1,0) and two far outside points.

#### Chris_M_Thomasson

• Fractal Feline
• Posts: 154
• Programmer by trade; love fractals and math! :^)
##### Re: The Multi-Julia...
« Reply #5 on: July 21, 2021, 09:20:24 AM »
Here are two attempts. The circular one uses 8 different parameter values, from the 1/9, 2/9, ..., 7/9, and 8/9 disk tangent points to the main cardioid. The other uses (-1,0) and two far outside points.

Oh wow: I am humbled by your results! Did you use equal probability factors to choose the Julia sets and/or roots? Using a far out point or two can really spice things up!

#### lkmitch

• Fractal Phenom
• Posts: 51
##### Re: The Multi-Julia...
« Reply #6 on: July 21, 2021, 06:44:33 PM »
Oh wow: I am humbled by your results! Did you use equal probability factors to choose the Julia sets and/or roots? Using a far out point or two can really spice things up!

Thanks! Yes, both images used equal probabilities. I haven't played around with unequal probabilities yet.

#### Chris_M_Thomasson

• Fractal Feline
• Posts: 154
• Programmer by trade; love fractals and math! :^)
##### Re: The Multi-Julia...
« Reply #7 on: July 22, 2021, 05:50:17 AM »
Thanks! Yes, both images used equal probabilities. I haven't played around with unequal probabilities yet.

Perfect! Okay. There are are lot of different fractals to explore in this multi Julia! Sorry for the moronic coloring, but check this one out at two Julia sets at points:

ct_complex jp_sets[2] = { { 0, 1 }, { 0, -1} }; // carpet

50/50 probability for the sets and the roots.

#### Chris_M_Thomasson

• Fractal Feline
• Posts: 154
• Programmer by trade; love fractals and math! :^)
##### Re: The Multi-Julia...
« Reply #8 on: July 22, 2021, 08:07:49 AM »
Here is a vector field plotted on the last fractal form:

#### Chris_M_Thomasson

• Fractal Feline
• Posts: 154
• Programmer by trade; love fractals and math! :^)
##### Re: The Multi-Julia...
« Reply #9 on: July 26, 2021, 10:54:25 PM »
Using a very crude color algo where I simply add a bit of color per visited pixel during iteration:

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