| 85904 | 640×480 | {{Information |Description = Mandelbrot set with period-2 bulb and main cardioid highlighted. |Source = I (~~~) created this work...
plane with Mandelbrot set //int ExtLastIteration; // unsigned char color; printf(" Setup \n"); iXmax= (int)(m*iSide); /* height of image in pixels */ iYmax...
{1}{2}}=\left\{w:abs(2w)=1\right\}} Cardioid ∂ H 1 {\displaystyle \partial H_{1}\,} is a boundary or period=1 hyperbolic component of Mandelbrot set g 1 {\displaystyle...
with Gnuplot. Boundaries of hyperbolic components of Mandelbrot sets are closed curves : cardioids or circles. Douady-Hubbard-Sullivan theorem (DHS) states...
AproximateMultiplierMap(c, period, EPS2, ER2); break; // } return w; } Note that period=0 denotes exterior of Mandelbrot set. Here different map ( Riemann...
circle to cardioid ( boundary of period 1 component of Mandelbrot set */ F(w):=w/2-w*w/4; /* circle D={w:abs(w)=1 } where w=l(t,r) t is angle in turns ;...
model of basilica Julia set draw main circle ( analog to main cardioid of Mandelbrot set) draw Ford circles on the main circle using Farey sequences as...
circle to cardioid ( boundary of period 1 component of Mandelbrot set */ F(w):=w/2-w*w/4; /* circle D={w:abs(w)=1 } where w=l(t,r) t is angle in turns ;...
point c is on the boundary of unit circle and can be mapped to the boundary of main cardioid of Mandelbrot set : c = c ( λ ) = λ 2 ( 1 − λ 2 ) ≈ − 0.390540870218399...
internal angle of parent CircleLevel : 0 = main circle (main cardioid) = period 1 cycle 1 = circles on the main circles 2 = stroke_width : A number without...
