Fractals
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Professor Korevaar
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FRACTALS!
There is a wonderful NOVA page about fractals, with links as well as an hour-long show. Go to http://www.pbs.org/wgbh/nova/fractals/.
Barnsley fern Java code to draw nice fern fractals.
Lecture Notes:
fractalpictures.pdf pictures and photographs of fractals and fractal-like structures in nature, math, and art.
scaling.pdf classical scaling and scaling with affine transformations .
classicalfractals.pdf classical fractals, before computers.
IFSfractals.pdf iterated function system fractals
Maple Procedures: This Maple 13 file (and a browser viewable .pdf copy) contains the procedures to define affine maps, draw the L-mapping picture, and generate iterated function system fractals. The procedures are illustrated with Sierpinski's triangle and an interesting bush-like fractal. The file also contains a procedure to make sure any questionable transformation in the system is actually a contraction.
FractalsMaple13.mw
FractalsMaple13.pdf
Art Gallery: These are some of my favorite student constructions, exported as ".jpg" files from Maple. The .pdf file has pictures of the jpg images below:
fractalexamps.pdf
algaetemp.jpg template
algae.jpg algae
crosstypetemp.jpg template
crosstype.jpg cross
diamondpatterntemp.jpg template
diamondpattern.jpg diamond pattern
flamewavetemp.jpg template
flamewave.jpg wave of flames
leavestemp.jpg template
leaves.jpg leaves swirling in the wind
mountaintemp.jpg template.
mountain.jpg mountain
pinetreetemp.jpg template.
pinetree.jpg snow-tinged pine tree
punkrockertemp.jpg template
punkrocker.jpg punkrocker hair
snowflaketemp.jpg template
snowflake.jpg complete Koch snowflake (First generate 1/3 of it, then rotate pieces to get entire flake.)
treetemp.jpg template.
tree.jpg Gothic tree.
weavetemp.jpg template
weave.jpg weave design for rug
fortificationtemp.jpg template
fortificationplan.jpg castle fortification floor plan
