A fractal is a geometric shape that when split into pieces, each part is a smaller version of the whole," a property called self-similarity. The term fractal was coined by Benoît Mandelbrot in 1975 from the Latin fractus meaning "broken" or "fractured." A mathematical fractal is an equation that undergoes iteration.

A fractal often exhibits:

• a fine structure
• mathematical irregularity
• self-similarity
• a Hausdorff dimension which is greater than its topological dimension
• a simple and recursive definition.

Fractals are considered to be infinitely complex. Natural objects that are approximated by fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, snow flakes, various vegetables (cauliflower and broccoli), and animal coloration patterns.

Fractal Reality

Maybe it was the holographic image of Princess Leia in Star Wars decades ago that inspired mass consciousness to explore the holographic nature of reality. Yet, as the saying goes, we are doomed to repeat history until we transcend the lessons of it. The mathematics reveal a beautiful symmetry - a truth that cannot be limited by words. A picture is worth a thousand words.

Explore, expand and breathe.

Fractal Artwork

Alexander Sphere

Dimensionality

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