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Welcome to the Mandelbrot Set, the mathematical wonder with more visual analogies to religious concepts than you can shake a holy book at! |
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Whereas science sports the equation... e = m x c2 this world of art comes from... e = m + e2 Amazing, isn't it! |
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This structure may be where peacocks get their feathers. |
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This tiny body, born in a starburst, contains infinte complexity, similar to but subtly different from any other such body in the set. |
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Perhaps an Amazonian tree sloth, high in the rain forest canopy, looks down on aboriginal huts and campfires here. It's an ordered forest, no doubt. |
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This view is haunting. It combines vague African totem themes with an echo of the Christian Cross. |
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This is the Mandelbrot Set in its entirety. All other images seen here come from magnifications within this field of view. Just magnify and color like a child. That's all. The symbolism: red - universe orange - earth black - egg yellow - womb green - the chorionic sac pink - inverted infant, prepared for birth |
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Order for order's sake is pretty. It's also mysterious. |
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Are those eyes staring out at us? Are the beings of the M-Set inviting us to chase them, but never to find? It's just one mystery of the infinite. |
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This is the Night Turtle Mother, bearing young on her back towards the sea.. She marches every night, every day. In infinite small variations, she reproduces and retires. At the bottom, left of center, note a somewhat lopsided or deformed-looking M-Set body. All are different, and only the collection of all such bodies -- the full, inclusive M-Set -- is perfectly symmetric. Perfection is all combined into one. |
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Spooky Queen with Tilted Crown Is she from Alice's world? If so, where is the Hatter? No doubt we'll find him. |
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Inspiration for fine porcelain plates. |
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OK, technically the M-Set is only the black points. Everything else is close-but-no-cigar. All this is done in the complex number plane. It's the coloring of the points that are almost in the M-Set that gives it its vibrant gloriousness. |
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Repeatedly invoking "e = m + e2 (which is more commonly written as "Z = Z2 + C" though there's no real difference) traces out the points in white. Points representing the trajectory of 'e' that start on black 'm' points (when e begins at zero) always keep their white lines in or near the black area of the core M-SET values. |
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Here's a view, from farther out, of the entire M-Set. |
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A point (which is to say, an initial 'm' value in the equation) which starts out not quite within the black of the true M-Set soon generates 'e' values that zip out of control and head off toward infinity. We color these points in accordance with how fast they "escape." |
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Anyone else get the feeling we're looking at a galaxy far, far away? |
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Colored another way, we see rivers, streams, and tributaries. All the M-Set bodies are connected! A little further coloring play would show a birth-to-senility aging process, where wrinkles grow with computational time spent on fleshing out an M-Set body. Totally computed and spent, an M-Set "body" desperately needs Botox! |
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An Octopus's Garden. It's not in the shade. |
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Kidneys. They cleanse the blood, perhaps, that runs through infinitely thin capillaries that bind this universe together. |
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Starry Night
Everywhere here where there is white, there is an M-Set body. A few dozen are identifiably visible. The rest turn into a blur, much the way the stars of the Milky Way are a blur to our eyes, but yet each separate star is there. The Milky Way only has maybe 400,000,000,000 stars. That's peanuts compared to the stars of the M-Set. Here, we're looking at infinity! |
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Desert Cactus. 'Nuf said. |
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Your guess is as good as mine. Magnify, and the spiral goes on forever! |
Here is a 3-minute "testimonial" Mandelbrot movie: Mandelbrot_Testimonial
Here is a 2-minute "dive to a galaxy far, far away": Mandelbrot_Galaxy
Here is a 5-minute combined Mandelbrot movie with instrumental music only: Mandelbrot_Music