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Post date: Apr 24, 2017 7:5:35 PM
Fractal geometry will make you see everything differently. There is a danger in reading further. You risk the loss of your childhood vision of clouds, forests, flowers, galaxies, leaves, feathers, rocks, mountains, torrents of water, carpet, bricks, and much else besides. Never again will your interpretation of these things be quite the same.
Fractals Everywhere (2000)
Mandelbrot set
Why is geometry often described as “cold” and “dry?” One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line… Nature exhibits not simply a higher degree but an altogether different level of complexity.
From The Fractal Geometry of Nature (1977)
What we did:
We continues from last week looking at the pattern of odd and even numbers in Pascals triangle. Surprisingly this pattern is like the Sierpinski triangle.
The we drew several steps of the Sierpinski triangle. Thes steps can be continued for ever the results shape is an example of a fractal.
Perhaps the most famous fractal is the Mandelbrot set. I showed this on a tablet and the kids got to zoom in and get a hint at the incredible complexity and beauty. Links below for apps.
Next week we'll talk in more detail about fractals and how they model many things in nature.
Things to try at home:
Carefully draw a Sierpinksi triangle. Experiment doing similar things with other shapes such as square or circles. Invent your own fractals and show me next time.
Play around with the apps below. Zoom into different places in the Mandelbrot set to find.
Family viewing! (just one simple equation make the most complex and beautiful object in existence) https://www.youtube.com/watch?v=ModQ59muXmU
Links:
There are many apps and webpages for exploring the Mandelbrot set and other fractals. Here are just some samples.
Web (make the number of iteration higher to get more detail. Draw a rectangle to zoom in)
Android
Mandelbrot Explorer
Fractview (click on the gallery icon to select different fractals or reset)
iphone/pad
Fractile plus (in options you can increase the iterations to get more detail when you zoom far)
Frax / FraxHD (many color and texture options for creating beautiful images.)
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