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Author Topic: Rococo No. 5  (Read 2438 times)
Description: A Mandelbrot with two transform sets
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element90
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« on: August 12, 2013, 11:54:28 AM »


https://copy.com/vZjmncSh0VyX

Produced using Saturn and Titan.

The standard Mandelbrot formula has the value of z transformed before each iteration, there are two transform sets A and B. Set A has one transform: power(8 + 0i), set B also has one transform: circle fold out(0.6) and the transform sequence is BBBBBA.

  
« Last Edit: May 23, 2014, 11:04:14 AM by element90, Reason: Replaced file links. » Logged

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cKleinhuis
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« Reply #1 on: August 12, 2013, 12:22:59 PM »

nice, what does the sequence mean ? is it applied all at the same time in that order, or is it went through in an alternating hybrid manner ?!
if so, i wonder if you hqave an option for sequencing the main formula as well wink
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element90
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« Reply #2 on: August 12, 2013, 01:14:19 PM »

The transform sequence controls how the transforms are applied. For iterations 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13 ... transform set B is applied to z before the Mandelbrot formula is evaluated, for iterations 6, 12, 18 ... transform set A is applied. I'm planning to write a piece about the use of transforms on my blog. One aspect of this particular fractal that isn't shown in this example is that there are "multibars" (derived from the name Multibar) as well as multibrots. The appearance of tricorns (or Mandelbars) are a feature of using the circle fold out transform when used applied to the Mandelbrot formula, adding the power transform into the mix turns them into multibars and multibrots.

Currently transform sets can be applied to a single fractal formula, most formulae include z = tranform(z) as an operation to be applied before the main formula, others include it as a part of the formula itself. There isn't a facility for switching between fractal formula, yet... I'm currently testing version 4.0.0 of Saturn and Titan so any new features will have to wait until the next release.


https://copy.com/ZcS2FZ3d8HsL
« Last Edit: May 23, 2014, 11:18:07 AM by element90 » Logged

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Kalles Fraktaler
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« Reply #3 on: August 12, 2013, 03:25:04 PM »

Very cool. Is this magnified or is it zoom 1? Is the black part inside the m-set?
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element90
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« Reply #4 on: August 12, 2013, 04:03:44 PM »

It is zoomed and the black is for locations that haven't escaped. Here's the full image:


https://copy.com/MFgWBkYYBPhA

Note the vague shape of the Mandelbrot, the holes are due to the circle fold out transform and the mass of buds due to the power transform. The interesting areas are in the two main holes towards what would have been the needle end of the Mandelbrot.

Two more examples:


https://copy.com/v8G0iaiFdRLr

https://copy.com/KUlw0xSwYnN7
« Last Edit: May 23, 2014, 11:26:55 AM by element90 » Logged

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