http://www.pbs.org/wgbh/nova/physics/mandelbrot-fractal.html


A printed interview (of text and images) with the mathematician that discovered/invented Fractal Geometry in the mid- 20th Century. Benoit Mandelbrot. With lots of very cool computer-genrated pictures using Fractal Geometry equations, which define "Dimension" very differently than Traditional Euclidean Geometry..

Euclid's Geometry relies on regular 'smooth lines' connecting points into basic shapes, like triangles, squares, rectangles, circles...

Mandelbrot's Fractal Geometry is based on observing Nature's "rough" shapes:

---Clouds are not actually smooth curves, but dynamic systems of water droplets in air currents.

---Rivers are not actually smooth boundaried waterways, but dynamic systems of water and its contents interacting with "earthen" materials.

---Trees and plants do not grow smoothly, but they do grow symetrically (with rough edges, as seen with a microscope).

---Lightning does not travel in a straight line, but in jagged directions with jagged edges.

---Shorelines are not smooth lines, but dynamically-changing minutely-complex self-repeating rough-edged patterns.

---Mountains are not smooth triangles, but fractal accretions and weathered dissolvements... etc.

Do Google searches for "fractal images" and "mathematical models"... it's a whole new universe of mathematical understandings...Raibow_fractcal_geometry_image.jpg



http://www.ss42.com/pt/fractle/fracdo.html

This is a "Fractal Fidget" paper model template for a dodecahedron printed with awesome color Fractal Art images. The creator suggested that it is a cool "fidget toy" to stare at while using your cell phone during a long conversation... I assume it copies well even when enlarged to handheld size...Because there's Lots to See in Those Patterns...


Fractal_Fidget.jpg



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Now that you met the Inventor of Fractals and Fractal Images, you could visit a Fractal Arts Website to see some more amazing New Geometry images...and then that leads you to the online tutorials for making your own computer Fractal Images...