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Kosmic-Stardust — Mandelbrot ABS Variations Complete Set of Formulas
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Published: 2014-10-19 13:15:20 +0000 UTC; Views: 7083; Favourites: 12; Downloads: 101
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Description
Complete Set of 12 Fractals, created by adding abs() commands to the standard form Mandelbrot fractal, and flipping the signage the imaginary side. The Asymmetric fractals such as Burning Ship and Buffalo have chiral pairs, created by reversing the signage on the imaginary side. Because these fractals create mirror images of each other, I have omitted them. The total including these dulpicates would make a set of 16. Negating the real side only generates duplicates of existing fractals with the needle pointing east. Those variants are also omitted.Most of these formulas are available in plugins for Fractal Extreme, created by Panzerboy in 2012. I supplied all the formulas in the fxmandelbarperp plugin.
sourceforge.net/projects/fxabs…
sourceforge.net/projects/fxmnd…
Feel free to incorporate any of the above fractal formulas in your own software.
Update:
Kalles Fraktaler was nice enough to add most of my formula to his awesome software:
www.chillheimer.de/kallesfrakt…
See Also:
2nd Order ABS Formula:
stardust4ever.deviantart.com/a…
3rd Order ABS Formula:
stardust4ever.deviantart.com/a…
4th Order ABS Formula:
stardust4ever.deviantart.com/a…
5th Order ABS Formula:
stardust4ever.deviantart.com/a…
Happy rendering!
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Comments: 8
What I noticed from most, if not all, of these, is that the first iteration of all of them seem to be a combination of the first iteration of the mandelbrot set and the mandelbar set arranged in zones like a pie centered at the origin.
An example of one of these would be the perpendicular burning ship, where the area above the x-axis follows a mandelbar patters and the area below follows a mandelbrot pattern.
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hey stardust, thx for this!
I remember seeing a video animation circling through all these at fractalforums.com, but I can't find it anymore - was that from you? if yo, do you have a link perhaps?
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I have no idea. Like, a zoom movie, or morphing from one formula o another?
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claude just found a tiny version of it over at fractalforums.org:
i.imgur.com/Zc3GrWv.gif
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no zoom involved, a full-view of the burning ship, where the tip on the x-axis slowly rotated 360 degrees, morphing the black area into different shapes, so you could see that the burning ship, celtic and if I remember correctly even the mandelbrot-set are basically just variation of the same formula.
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Sorry for the late reply. Yes, the Burning Ship is Chiral (meaning a left-handed and right-handed version exists). applying the abs() function to the R or I side of the formula has the effect of mirroring the coordinate across the x or y axis. A sign change on the Burning Ship flips it. A sign change on the Celtic Mandelbrot creates the Celtic Mbar.
Mandelbrots have randomly orientated minibrots hidden inside. The Burning Ship, Celtic, and Celtic Mbar form a similar group with similar shaped minis when the complex orientation is approximately at right angles. The Mandelbrot and Mandelbar are 180 degrees of flip. There is no mosaic effect as the Mbar has no abs() command. As a result, all minis are perfectly formed mandelbrots and mandelbars.
The Perpendicular Mandelbrot shares a similar grouping with minis shaped like the perpendicular, perpendicular burning ship and the Heart brot. The Heart fractals are rather boring, acting as a deflated Madelbrot with only mini hearts on the needle. It is similar to the bottom half of the burning ship.
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