Fractals: introduction

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

Sierpiński carpet#

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

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

SierpinskiCarpet3 \(\quad\) SierpinskiCarpet5

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

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

Dragon curve#

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

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

DragonCurve_10 \(\quad\) DragonCurve_50

Left figure: Dragon Curve, 10000 points

Right figure: Dragon Curve, 50000 points

Barnsley’s Fern#

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

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

BarnsleyFern_20 \(\quad\) BarnsleyFern_100

Left figure: Barnsley’s Fern, 20000 points

Right figure: Barnsley’s Fern, 100000 points

Contents