Lecture 7 and 8
Fractals
1. Here is an interactive tree fractal that we have already seen (January 16 lecture) - as you might recall, the "best" tree is obtained if we choose the ratio of the consecutive branches to be 1/Golden Ratio.
2.An interactive page where you can explore 5 fractals: Koch snowflake, Dragon curve, a tree fractal depicted in the textbook, a "crystal" also seen in the textbook, and the Hilbert curve.
3. A gallery of beautiful fractals - all are home made. These are related to the Julia sets (associated with some special rearrangements of the points in the plane which are neither similarities nor isometries). Some details explained in class.
(a) Here is the basic Mandelbrot fractal.
(b) Some beautifull fractals; it is math that generates them.
For the Sierpinski gasket and Menger sponge go to the Animation Gallery
4. Movies. (Click on the tumbnail to see the movie)
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© Sasho Kalajdzievski
