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element90 — Mosaic Mandelbrot
Published: 2012-03-09 09:10:08 +0000 UTC; Views: 965; Favourites: 22; Downloads: 0
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Description
This isn't what it seems, none of the points in this image have escaped so the colouring is all inner. The formula is the natural logarithm of the Mandelbrot formula.Titan Version 2.0 development
Parameters
Formula: Lzcpac
z = transform(z)
z = log(z^alpha + c)
alpha = 2 + 0i
Programs: saturn and titan
Number of A transforms: 0
Number of B transforms: 0
Transform sequence: A
Number of Complex Plane transforms: 0
Initial values of z: 0 + 0i
Image centre: 0.397481642666666667 + 0.13554688i
Image width: 0.0027776
Rotation about image centre: 0 degrees
Maximum iterations: 260
Bailout: No Bailout
Colour selection: all points are inner
Outer colouring: iteration
Inner colouring: absolute log of variance of magnitude
Related content
Comments: 15
An infinite zoom in feature would be perfect.
Otherwise awesome job
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Currently Saturn and Titan use long doubles so zooming is limited to the precision of type, the use of arbitrary precision numbers is problematic, the execution time in considerably increased and there is a lack of functions provided i.e. no sin, cos, tan etc., so "infinite" zoom would be restricted to fractals that are implemented using simple arithmetic operations and simple colouring methods.
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That's interesting 
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I've seen these crop up quite a lot in areas of "captive" orbits, it also happens with Tricorns.
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Here's one with both [link]
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You are a master in finding them (I've already faved it). See also my journals [link] and [link] if you feel for it
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It's pretty accidental, I suppose it is due to the experimentation with transforms that I can apply to all the escape time fractals in my programs, several of these transforms result in captive orbits so I have to resort to inner colouring methods hence the frequent discovery of Mandelbrot and Tricorn shapes in areas of captive orbits. I've had a look at your journal articles, the pictures are as always worth a look but the technicalities are beyond me.
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There are SO much breaking stuff coming out accidental
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No probs, your technicals are at the moment beyond me too, but anyhow interesting
BTW, I don't remember if I mentioned this [link] journal (another interesting phenomena)
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I've already seen the journal article on ghost Mandelbrots, you mentioned it in an earlier exchange of messages.
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This comment is going to look very dumb next to all the math and work you put into making this, but I seriously just love the way it looks like the veins in a leaf...
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