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Center is at (c,0), so |z-c|=|c| so c = |z|^2/2Re(z) = 1/r

unsigned char ComputeColor(complex double z){ double r; // r = (2Re(z))/|z|^2 r = 2.0*creal(z)/ (cabs(z)*cabs(z)); while ( r>1.0) r -=1.0; return r*255; // 8- bit color = shades of gray}