Newton/Julia Fractal (1714)
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Dr. Michael's function f(z) = (z^3+(0.5+0.78*i)*z/(z+1)
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Infinite Douady's Lapin?
f(z) = (z^5-(0.05+0.0702*i)*z+0.09)/z^3
Newton/Julia Fractal (1715)
Again Becker's Dragon
f(z) = (z^3+(0.51+0.78*i)*z)/(z+1)+0.005
Newton/Julia Fractal (1716)
Becker's Tag Crest
f(z) = z^4/(0.5*z^12+z^8+0.6223*z^4+0.0001)
Newton/Julia Fractal (1717)
f(z) = z^4/(0.14*z^12+z^8+0.635*z^4+0.0001)
Newton/Julia Fractal (1718)
f(z) = z^4/(0.274*z^12+0.5*z^8+0.635*z^4+0.0001)
Newton/Julia Fractal (1719)
f(z) = (z^5-z)/(0.778*z^2+1)
Sonate K3078
Sonate K3079
Newton/Julia Fractal (1720)
f(z) = (z^3+z)/((-0.1+i)*z^2+1)+0.01
Sonate K3081
Sonate K3082
Dr.Michael Becker
f(z) =( z^3-z)/(d*z^2+1) mit d=-0.003+0.995i, dargestellt auf [-7;7]x[-7;7].
Here the absolute value of d is smaller than 1, so that Infinity is in the Fatou set. Near 0 there are again to petals. Near Infinity the function behaves as z->-iz, so that the number of spirals, which run direction Infinity is exactly four. Probably the four turning points of the spirals form a repelling cycle of period 4.
Sonate K3083
f(z) = (z^3+z)/((-0.3+0.995*i)*z^2+1)+0.01
Newton/Julia Fractal (1721)
Michael Becker Function
f(z) = (z^3+z)/((-0.003+0.995*i)*z^2+1)