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| Paul Carlson: Star of David | Star of David v2 | Star of David v3 (detail) |
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Spot Light Corner: Paul Carlson's Star of David Orbit-Trap Fractals never stop surprising me. More then any other form of art fractal pictures are the art of the unexpected, derived from the universal Chaos. So imagine my surprise when I saw this strict geometrical orderly sign - the six-pointed star, which is also called "Star of David". I soon discovered that this star of David design is created with a complex "orbit-trap", that was developed about a year ago by the ingenious artist and programer Paul Carlson. As Paul told me, this formula was a further development from the concept of "orbit traps", that Paul has invented some six years ago. All the amazing pictures on this page were done by Paul, using his own Star of David trap. So I think it will be best to let Paul describe and explain the works by himself: "The last fractal rendering method I devised (about a year ago) is the one I named "Star of David" (for obvious reasons). It was perhaps the rendering method most difficult to program. I'm posting these images of "Star of David Fractals" because they quite different and, to me anyway, interesting. The first image (v1, top-left) shows the whole Mandelbrot Set. Notice that there is little or no distortion in the large star. In the zoomed-in image to follow, (v2, top-center) the stars become distorted in the way you would expect, being stretched towards the minibrot in the center of the image. Because the orbit trap is centered on the origin of the complex plane, every star has a minibrot at it's center. The third one (v3, top-right) is a Star of David rendering, applied to a Barnsley-Julia set." |
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| Star of David v4 | Star of David v5 (detail) | Star of David v6 |
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On the second row of picture we the clean-cut orderly sis-pointed star begins to pass through a series of trasformations and distortions, to render these lovely pictures: "The image (v5, above, center) is a zoom into a 4th-order Newton's method Mset. In the image (v6, above right) I applied the Star of David rendering to a third-order Chebyshev approxomation equation, that stacked up the stars with some interesting twists." |
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| Star of David v7 | Star of David v8 |
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In the above two pictures the distortion cause by the Star of David trap is so enormous, that the typical six-pointed pattern of the star is not recognized any more. Even as you know that it was created with this trap, it is quiet difficult to notice them, though with some good will, still possible. And here is how Paul describes these two last pictures:
"I'm including this one (v7, above-left) as an afterthought to show how, in very deep zooms (this image has a magnification of 41227791514), the stars become distorted beyond all recognition, and yet can still produce a passable image. And last a spiral (v8, above-right) in a Julia set of the Pokorny equation. The stars are distorted beyond recognition, but the image is kind of nice." The curator August 2000 |