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Fractals: introduction
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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




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Sierpiński carpet
---------------------------------------------


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

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




|SierpinskiCarpet3| `\quad` |SierpinskiCarpet5|

.. |SierpinskiCarpet3| image:: ../_static/Combining2D3D/FractalIntro/SierpinskiCarpet3.*
   :width: 47%

.. |SierpinskiCarpet5| image:: ../_static/Combining2D3D/FractalIntro/SierpinskiCarpet5.*
   :width: 47%



**Left figure**: Sierpiński carpet, `n = 3`.


**Right figure**: Sierpiński carpet, `n = 5`.







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Dragon curve
---------------------------------------


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

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




|DragonCurve_10| `\quad` |DragonCurve_50|


.. |DragonCurve_10| image:: ../_static/Combining2D3D/FractalIntro/DragonCurve_10.png
   :width: 47%


.. |DragonCurve_50| image:: ../_static/Combining2D3D/FractalIntro/DragonCurve_50.png
   :width: 47%


**Left figure**: Dragon Curve, 10000 points


**Right figure**: Dragon Curve, 50000 points




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Barnsley's Fern
---------------------------------------



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

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




|BarnsleyFern_20| `\quad` |BarnsleyFern_100|

.. |BarnsleyFern_20| image:: ../_static/Combining2D3D/FractalIntro/BarnsleyFern_20.png
   :width: 47%

.. |BarnsleyFern_100| image:: ../_static/Combining2D3D/FractalIntro/BarnsleyFern_100.png
   :width: 47%


**Left figure**: Barnsley's Fern, 20000 points


**Right figure**: Barnsley's Fern, 100000 points