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
Julia sets, example 1: Classical set#
The Python code for the example below, without using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D01a_Julia01.py, and the XML code in the file D01a_Julia01.2D.xml.
The Python code for the example below, using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D01b_Julia01.py, and the XML code in the file D01b_Julia01.2D.xml.
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”.
Julia sets, example 2: Glynn fractals#
The Python code for the example below, without using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D02a_Julia02.py, and the XML code in the file D02a_Julia02.2D.xml.
The Python code for the example below, using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D02b_Julia02.py, and the XML code in the file D02b_Julia02.2D.xml.
See also: http://www.3d-meier.de/, Mandelbrot und Julia Mengen
Julia sets, example 3: Spiral Septagon fractal#
The Python code for the example below, without using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D03a_Julia03.py, and the XML code in the file D03a_Julia03.2D.xml.
The Python code for the example below, using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D03b_Julia03.py, and the XML code in the file D03b_Julia03.2D.xml.
See also: https://paulbourke.net/fractals/septagon/
Julia sets, example 4: Reuleaux Triangle fractal#
The Python code for the example below, without using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D04a_Julia04.py, and the XML code in the file D04a_Julia04.2D.xml.
The Python code for the example below, using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D04b_Julia04.py, and the XML code in the file D04b_Julia04.2D.xml.
See also: https://paulbourke.net/fractals/triangle/
Julia sets, example 5: Phoenix Julia fractals#
The Python code for the example below, without using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D05a_Julia05.py, and the XML code in the file D05a_Julia05.2D.xml.
The Python code for the example below, using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D05b_Julia05.py, and the XML code in the file D05b_Julia05.2D.xml.
Compare this with “Marek Dragon”
See also: https://paulbourke.net/fractals/phoenix_julia/
Julia sets, example 6: Cubic Julia fractals#
The Python code for the example below, without using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D06a_Julia06.py, and the XML code in the file D06a_Julia06.2D.xml.
The Python code for the example below, using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D06b_Julia06.py, and the XML code in the file D06b_Julia06.2D.xml.
See also: https://paulbourke.net/fractals/cubicjulia/
Julia sets, example 7: Spiral Julia fractal (uses \(z_{n+1} = \tan(z_n^2 +c)\))#
The Python code for the example below, without using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D07a_Julia07.py, and the XML code in the file D07a_Julia07.2D.xml.
The Python code for the example below, using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D07b_Julia07.py, and the XML code in the file D07b_Julia07.2D.xml.
See also: https://paulbourke.net/fractals/spiraljulia/
Julia sets, example 8: 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
See also: http://www.3d-meier.de/, Mandelbrot und Julia Mengen, 4.7. zn+1 = c sin(zn)
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/
The Python code for the example below, without using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D08a_Julia08.py, and the XML code in the file D08a_Julia08.2D.xml.
The Python code for the example below, using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D08b_Julia08.py, and the XML code in the file D08b_Julia08.2D.xml.
Julia sets, example 9: Julia09 fractals#
The Python code for the example below, without using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D09a_Julia09.py, and the XML code in the file D09a_Julia09.2D.xml.
The Python code for the example below, using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D09b_Julia09.py, and the XML code in the file D09b_Julia09.2D.xml.
See also: https://paulbourke.net/fractals/cubicjulia/
Julia sets, example 10: Julia10 fractals#
The Python code for the example below, without using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D10a_Julia10.py, and the XML code in the file D10a_Julia10.2D.xml.
The Python code for the example below, using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D10b_Julia10.py, and the XML code in the file D10b_Julia10.2D.xml.
See also: https://paulbourke.net/fractals/cubicjulia/
Julia sets, example 11: Julia11 fractals#
The Python code for the example below, without using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D11a_Julia11.py, and the XML code in the file D11a_Julia11.2D.xml.
The Python code for the example below, using numba, can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D11b_Julia11.py, and the XML code in the file D11b_Julia11.2D.xml.
See also: https://paulbourke.net/fractals/cubicjulia/
