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# Category: Complex Analysis
# Name: Newton Fractal
#
# Draw the basins of attraction of running the Newton algortihm
# with different starting point for computing the third root.
# The three roots are drawn in three different colors
#
iterations = 10;
LinePlotWindow = [-2,2,-2,2];
LinePlotDrawLegends = false;
PlotWindowPresent(); # Make sure the window is raised
points1 = null;
points2 = null;
points3 = null;
k1 = 1;
k2 = 1;
k3 = 1;
function DrawThePlot () = (
PlotCanvasFreeze ();
LinePlotClear ();
LinePlotDrawPoints (points1, "color", "blue", "thickness", 3);
LinePlotDrawPoints (points2, "color", "red", "thickness", 3);
LinePlotDrawPoints (points3, "color", "green", "thickness", 3);
PlotCanvasThaw ();
);
for x = -2.0 to 2.0 by 0.02 do (
for y = -2.0 to 2.0 by 0.02 do (
c = z = x+1i*y;
for m=0 to iterations do (
z = z-(z^3-1)/(2*z^2);
if |z-1| < 0.5 then (
points1@(k1,) = [Re(c),Im(c)];
increment k1;
break
) else if |z-(-0.5+0.866025403784i)| < 0.5 then (
points2@(k2,) = [Re(c),Im(c)];
increment k2;
break
) else if |z-(-0.5-0.866025403784i)| < 0.5 then (
points3@(k3,) = [Re(c),Im(c)];
increment k3;
break
)
);
# every 1000 point display intermediate picture
if (k1+k2+k3) % 1000 == 0 then (
DisplayVariables(`k1,`k2,`k3);
DrawThePlot()
)
)
);
DrawThePlot();
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