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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