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Inflection mappings
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Description: Morphing a basic Mandelbrot-shape 30 times, which would require a zoom depth of E1406173.
But this image is actually out-zoomed.
Points are transformed according to this
Code:

// Get the points in the mandelbrot for the screen coordinates
r = r_start+x*(r_stop-r_start)/nX;
i = i_start+y*(i_stop-i_start)/nY;

// Transform the coordinates for each inflection point
int inf;
for(inf=g_nInflections-1;inf>=0;inf--){
if(r>g_pInflections[inf].r){
r = g_pInflections[inf].r - (r-g_pInflections[inf].r);
i = g_pInflections[inf].i - (i-g_pInflections[inf].i);
}
double ratio = (double)(i-g_pInflections[inf].i)/(double)(r-g_pInflections[inf].r);
double degree = -atan(ratio);
double dist = sqrt((double)((r-g_pInflections[inf].r)*(r-g_pInflections[inf].r)+(i-g_pInflections[inf].i)*(i-g_pInflections[inf].i)))/diagonal;
double dr = (double)g_pInflections[inf].r + (double)(r-g_pInflections[inf].r)*cos(degree)*dist
+ (double)(i-g_pInflections[inf].i)*sin(degree)*dist;
double di = (double)g_pInflections[inf].i + (double)(i-g_pInflections[inf].i)*cos(degree)*dist
- (double)(r-g_pInflections[inf].r)*sin(degree)*dist;
r=dr;
i=di;
}

// Contiunue with the ordinary mandelbrot calculation sequence

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Filesize: 142.62kB
Height: 720 Width: 1280
Discussion Topic: View Topic
Keywords: Inflection mappings
Posted by: Kalles Fraktaler January 27, 2017, 10:41:57 AM

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