Monday, 7 April 2014

Barnsley fern


The Barnsley Fern was created by Michael Barnsley using an iterated function system.
Barnsley's Fern animated

















The attractor of the iterated function system given by the set of "fern functions"
f_1(x,y)=[0.85 0.04; -0.04 0.85][x; y]+[0.00; 1.60]
(1)
f_2(x,y)=[-0.15 0.28; 0.26 0.24][x; y]+[0.00; 0.44]
(2)
f_3(x,y)=[0.20 -0.26; 0.23 0.22][x; y]+[0.00; 1.60]
(3)
f_4(x,y)=[0.00 0.00; 0.00 0.16][x; y]


 references : http://mathforum.org/mathimages/index.php/Barnsley_Fern
                     http://math.kendallhunt.com/documents/precalculus3/Activities/Barnsley%27s%20Fractal%20Fern%20Worksheet.pdf
http://mathworld.wolfram.com/BarnsleysFern.html












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