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Welcome to Fractal Forums > Fractal Software > General Discussion > The Mandelbox
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Author Topic: The Mandelbox  (Read 1371 times)
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paolo
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« on: January 03, 2014, 12:03:08 AM »
 grin Wouldn't it be lovely if there is a way of generating an imaginary power or complex power Mandelbox if this is possible?
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Tglad
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« Reply #1 on: January 03, 2014, 12:35:38 AM »
Did you mean Mandelbrot? There is no power in a mandelbox... just folding and scaling... the equivalent of a higher power would be I suppose to fold and scale several times before adding c... I haven't tried that.
However, it is quite mind bending to get an equivalent of an imaginary or complex power.

Even for mandelbrot and julia sets it doesn't really work to choose an imaginary or complex power because they are multi-valued, the arbitrary choice of which value to pick leads to discontinuities. You could choose all of them, but it would be slow and you'd probably get a ghosting of many images like the buddhabrot.
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cKleinhuis
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« Reply #2 on: January 03, 2014, 01:57:42 AM »
i tested it in ultrafractal2d, it somehow behaves like expected, repeating the folding and scaling
resolves an alternation between squared shape and circle shape, the square shapes behave like expected, the features become more densely populated:

* mandelbox2_standard.jpg (65.46 KB, 640x480 - viewed 349 times.)

* mandelbox2_power3.jpg (27.6 KB, 640x480 - viewed 359 times.)

* mandelbox2_power4.jpg (38.51 KB, 640x480 - viewed 369 times.)

* mandelbox2_power5.jpg (58.21 KB, 640x480 - viewed 351 times.)
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