Fractals related to the Julia set#
See also: http://www.3d-meier.de/, Mandelbrot und Julia Mengen
See also: https://en.wikipedia.org/wiki/Julia_set
Classical Julia set#
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See also: http://www.3d-meier.de/, Mandelbrot und Julia Mengen
See also: https://paulbourke.net/fractals/sinjulia/julia_set.py (contains suggestions for \(c\).) in the section “QUADRATIC JULIA ITERATION AND BAILOUT”.
Glynn fractals#
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See also: http://www.3d-meier.de/, Mandelbrot und Julia Mengen
Spiral Septagon fractal#
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See also: https://paulbourke.net/fractals/septagon/
Reuleaux Triangle fractal#
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See also: https://paulbourke.net/fractals/triangle/
Phoenix Julia fractals#
Compare this with “Marek Dragon”
See also: https://paulbourke.net/fractals/phoenix_julia/
Cubic Julia fractals#
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See also: https://paulbourke.net/fractals/cubicjulia/
Spiral Julia fractal (uses \(z_{n+1} = \tan(z_n^2 +c)\))#
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See also: https://paulbourke.net/fractals/spiraljulia/
Julia set of \(\sin(z)\)#
To do this we form the series \(zk+1 = c sin(zk)\), starting with some initial \(z0\).
See also: https://paulbourke.net/fractals/sinjulia/julia_set.py
The behaviour of this series determines whether or not the initial z0 is part of the julia set or not. More precisely, if the series tends to infinity then z0 is part of the Julia set, otherwise it isn’t. In the examples shown on the right the white regions are in the Julia set, black points are outside the Julia set.
To create images of the Julia set we map pixels in the image onto values of z0 and colour the pixel dependent on the behaviour of the series. In the examples on the right the image is mapped onto the range +-2pi in both the real and imaginary axes. The series is tested after 50 terms, it is decided that it tends to infinity if the absolute value of the imaginary part of zk is greater than 50.
See also: https://paulbourke.net/fractals/sinjulia/
See also: http://www.3d-meier.de/, Mandelbrot und Julia Mengen, 4.7. zn+1 = c sin(zn)
Julia09 fractals#
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See also: https://paulbourke.net/fractals/cubicjulia/
Julia10 fractals#
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See also: https://paulbourke.net/fractals/cubicjulia/
Julia11 fractals#
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See also: https://paulbourke.net/fractals/cubicjulia/
