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An Introduction to the Fascinating Patterns of Visual Math
(Updated Jan 2010)

Platonic / Vectoral Geometry
The geometry of 3-D faceted symmetrical shapes, composed of faces, edges and vertexes. They reflect the fundamental properties of empty space.
Platonic / Vectoral Geometry

Very Simple Iterative Fractals
Fractals are patterns that repeat themselves; the simples examples are the triangular subdivision and branching patterns below, ...
Simple Iterative Fractals

Natural fractals
Most all patterns in nature are fractals - galaxies, plants, mountains, coastlines, snowflakes, arteries, nerves, lungs, clouds, rivers, seashells ....
Fractals in nature


Multi Dimensional Forms

No longer sci-fi - multiple dimensions are an accepted & proven fact of mathematics and physics. The $1,000,000 question is "how many exist?"
Multi Dimensional Forms


The Famous Mandelbrot Set

This is arguably the most gorgeous, intricate & popular fractal yet discovered. It also has cryptic relationships to magnetism and dimensionality.
The Famous Mandelbrot Set

Visual Guide to the Mandelbrot Set
(NEW Jan 2010) A basic guide to the wide variations of patterns & names of various regions of the Mandelbrot set. Seahorses, needles, spirals, etc.
Guide to the Mandelbrot Set


PHI - the Golden Ratio

'the Golden Mean', this ratio is 1 to 1.618. In the pic below each square is 1.618 x the size of the next. This pattern appears everywhere, even your body!.
PHI - the Golden Ratio

Categories & Types Of Fractals

(NEW Jan 2010) There are many mathematical functions that can produce interesting fractals. mandel & julia sets, chaotic attractors, IFS & more
Categories & Types Of Fractals

New 3 Dimensional Fractal Explorations

(NEW Jan 2010) Fractals can be visualized in any number of dimensions. traditional fractals are viewed on a 2D plane, but new visualizations are changing that. New 3 Dimensional Fractal Explorations

Wada Basin Sphere Fractals

The secret life of mirrored spheres seen from the inside. Place a camera in-between spheres and an intricate fractal 'wada basin' appears - amazing!
Wada Basin Sphere Fractals


Fractal Technology & Historical Fractals

Fractals occur in art throught history yet they have only been formally defined in the late 20th century. Amazing Fractal technology is now being developed.
Fractal Technology & Historical Fractals

Other Fractals & Cool Patterns

(NEW Jan 2010) There are many fractal, geometric and quasi-periodic forms that are quite interesting to discover and contemplate. Also hand-painted acrylic fractal forms!
Other Fractals & Cool Patterns

 

Minimal Surfaces

Nature always conserves space & energy; soap bubbles and wire-frames were first used to observe the dynamics of space conserving shapes
Minimal Surfaces
 


Fractal Art Image Gallery

Fractal Art Image Gallery


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Paul Laffoley Posters

 
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