bkercso
Fractal Lover
Posts: 220


« Reply #15 on: June 01, 2016, 10:51:50 PM » 

Img #7: coupling=1E4 Img #8: Coupled 0.1*Mandelbrot + 0.9*Burning ship (started both from (0,0) @ constant (x0,y0) )


« Last Edit: June 16, 2016, 12:04:01 AM by bkercso »

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bkercso
Fractal Lover
Posts: 220


« Reply #16 on: June 01, 2016, 11:39:40 PM » 

Coupled Mandelbrot + Burning ship:Initial values:
x=0; y=0; x2=0; y2=0;
Iterations:
xtemp:=sqr(x)sqr(y)+x0; { Mandelbrot } ytemp:=2*x*y+y0; x2temp:=sqr(x2)sqr(y2)+x0; { Burning ship } y2temp:=2*abs(x2*y2)+y0;
x:=xtemp+coupling*(x2tempxtemp); y:=ytemp+coupling*(y2tempytemp); x2:=x2temp+coupling*(xtempx2temp); y2:=y2temp+coupling*(ytempy2temp); zk:=sqr(x)+sqr(y);
Img #9: Zoom of the above. It combines the emblematic patterns of Mandelbrot and Burning ship. It not was easy to find such a picture; I found it in the positive half of the imag. axis. center (Re), center (Im), range (Re), range (Im): 1.7105465724241176E+0000 4.2582773728477242E0003 9.7538511027023023E0010 6.5025674018015351E0010


« Last Edit: June 02, 2016, 02:39:16 AM by bkercso »

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claude
Fractal Bachius
Posts: 563


« Reply #17 on: June 02, 2016, 01:20:28 AM » 




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bkercso
Fractal Lover
Posts: 220


« Reply #18 on: June 02, 2016, 01:30:17 AM » 

Wow, cool! You did a different thing than me, because I don't adjust the constant, but the initial values of x and y. At 1st set (x,y)=(0,0), at 2nd set (x2,y2)=(c.re,c.im), where c.re, c.im the constants for both sets. This is equal with 1 iteration between the sets.



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bkercso
Fractal Lover
Posts: 220


« Reply #19 on: June 02, 2016, 01:39:42 AM » 

3 coupled Mandelbrot sets with symmetric "hierarchical" coupling:
3 coupled Mandelbrot set:
Initial values:
x:=0; y:=0; x2:=x0; y2:=y0; { = 1 iteration } x3:=sqr(x0)sqr(y0)+x0; y3:=2*x0*y0+y0; { = 2 iterations }
Iteration: xtemp:=sqr(x)sqr(y)+x0; ytemp:=2*x*y+y0; x2temp:=sqr(x2)sqr(y2)+x0; y2temp:=2*x2*y2+y0; x3temp:=sqr(x3)sqr(y3)+x0; y3temp:=2*x3*y3+y0;
x:=xtemp+coupling*(x2tempxtemp+coupling*(x3tempxtemp)); y:=ytemp+coupling*(y2tempytemp+coupling*(y3tempytemp)); x2:=x2temp+coupling*(x3tempx2temp+coupling*(xtempx2temp)); y2:=y2temp+coupling*(y3tempy2temp+coupling*(ytempy2temp)); x3:=x3temp+coupling*(xtempx3temp+coupling*(x2tempx3temp)); y3:=y3temp+coupling*(ytempy3temp+coupling*(y2tempy3temp)); zk:=sqr(x)+sqr(y);
Img #10: 3 coupled Mandelbrot sets with symmetric "hierarchical" coupling (coupling=0.001): "second generation" hybride patterns


« Last Edit: June 02, 2016, 01:25:35 PM by bkercso »

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claude
Fractal Bachius
Posts: 563


« Reply #20 on: June 02, 2016, 02:00:08 AM » 

Wow, cool! You did a different thing than me, because I don't adjust the constant, but the initial values of x and y. At 1st set (x,y)=(0,0), at 2nd set (x2,y2)=(c.re,c.im), where c.re, c.im the constants for both sets. This is equal with 1 iteration between the sets. aha! thanks for the explanation, makes more sense



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bkercso
Fractal Lover
Posts: 220


« Reply #21 on: June 02, 2016, 02:22:57 AM » 

Cheers! Img #11: Finally, there already are divergent regions on the edge of these spirals at these 3 coupled sets: Img #12: Where the mixed / hybride patterns are Img #13: a zoom of Img #12


« Last Edit: June 02, 2016, 02:37:31 AM by bkercso »

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Chillheimer


« Reply #22 on: June 02, 2016, 11:03:00 AM » 

wow, guys you are doing awesome and probably groundbreaking work here! keep it up!



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 Fractals  add some Chaos to your life and put the world in order. 



Max Sinister


« Reply #23 on: June 02, 2016, 10:53:37 PM » 

@claude: Your images look as if Fragmentarium wanted to honor its name (OK, there's a bad pun implied by me).



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bkercso
Fractal Lover
Posts: 220


« Reply #24 on: June 03, 2016, 01:38:32 AM » 




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bkercso
Fractal Lover
Posts: 220


« Reply #25 on: June 03, 2016, 02:52:28 AM » 

Sinusoidal coupling: Sinusoidal coupling:
coupling=coupling_original*(sin(iterationNumber*frequency)+1)/2;
Img #14: 2 coupled Mandelbrot sets with sinusoidal coupling, coupling=0.01, frequency=0.01 Img #15: coupling=0.01, frequency=0.001 Img #16: Zoom of the above, coupling=0.01, frequency=0.001 (maxiter=8000); empty patterns... Img #17: coupling=0.01, frequency=0.01


« Last Edit: June 04, 2016, 02:24:32 AM by bkercso »

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0Encrypted0


« Reply #26 on: June 03, 2016, 05:27:19 AM » 

Last month, I attended the International Fractal Art Symposium, where Christian Kleinhuis gave a talk on hybrid fractalseither alternating or interpolating functions each iteration. Since I already have an alternating functions formula in the UF formula database, I decided to write an interpolating functions formula. You can find it in lkm3.ufm and there are some sample parameter sets in lkm3.upr. The attached image is one example, interpolating between 2 Newtons functions, 2 Mandelbrot, and 2 Julia on each iteration.
Would someone please give a brief explanation of the difference between alternating, interpolating and coupled formulas?



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bkercso
Fractal Lover
Posts: 220


« Reply #27 on: June 04, 2016, 02:29:35 AM » 

I edited the pictures in Reply #25, because my program contains an error (I called a local and a global variable with the same name). This sin (or cos) coupling results partially empty patterns. Img #18: And a new image with cos coupling at a place from Video #1: coupling:=1E4*(1E3*cos(iterationNumber*1E3)+1)


« Last Edit: June 05, 2016, 01:04:12 AM by bkercso »

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bkercso
Fractal Lover
Posts: 220


« Reply #28 on: June 04, 2016, 02:39:32 AM » 

Img #19: this is without sin coupling, just simple coupled Mandelbrots (2 sets): Set: (place of Img #15, without sinusoidal modulations of coupling) Zoom:



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bkercso
Fractal Lover
Posts: 220


« Reply #29 on: June 05, 2016, 02:03:28 AM » 

3 different coupling for Img #18: Img #20: original image, simple coupling coupling: 1E4
Img #18 (again): coupling with cosinus ripple coupling:=coupling_original*(1+Amplitude*cos(iterationNumber*Frequency));
coupling_original: 1E4 Amplitude=Frequency: 1E3 // relative amplitude
Img #21: coupling with random ripple (the same random number series was used for each pixel) coupling:=coupling_original*(1+Amplitude*(random0.5)*2); // @each iteration
coupling_original: 1E4 Amplitude: 1E3 // relative amplitude random: 0..1
The image is not reproducible, depends on the values of the random number series


« Last Edit: June 05, 2016, 10:36:54 AM by bkercso »

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