Fractals: introduction

See also: http://www.juliasets.dk/Pictures_of_Julia_and_Mandelbrot_sets.htm

See also: http://www.3d-meier.de/, Mandelbrot und Julia Mengen

See also: http://www.dhushara.com/DarkHeart/quasif/quasi.htm (includes Kleinian fractals)

Difference Method: https://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/demm

MandelbrotSetExterior: https://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/MandelbrotSetExterior#Real_Escape_Time

Fractals/fractalzoomer: https://en.wikibooks.org/wiki/Fractals/fractalzoomer

https://en.wikipedia.org/wiki/Fractal

Barnsley’s Fern

https://mathworld.wolfram.com/BarnsleysFern.html

https://en.wikipedia.org/wiki/Barnsley_fern

The Python code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D01_BarnsleyFern.py, and the XML code in the file D01_BarnsleyFern.2D.xml.

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Left figure: Barnsley’s Fern, 20000 points

Right figure: Barnsley’s Fern, 100000 points

Dragon curve

https://en.wikipedia.org/wiki/Dragon_curve

https://mathworld.wolfram.com/DragonCurve.html

The Python code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D02_DragonCurve.py, and the XML code in the file D02_DragonCurve.2D.xml.

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Left figure: Dragon Curve, 10000 points

Right figure: Dragon Curve, 50000 points

Sierpiński carpet

https://en.wikipedia.org/wiki/Sierpi%C5%84ski_carpet

https://mathworld.wolfram.com/SierpinskiCarpet.html

The Python code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D03_SierpinskiCarpet.py, and the XML code in the file D03_SierpinskiCarpet.2D.xml.

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Left figure: Sierpiński carpet, \(n = 3\).

Right figure: Sierpiński carpet, \(n = 5\).