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Author Topic: How much does order of hybrids and iteration count matter?  (Read 1695 times)
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wolfwing1
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« on: August 04, 2011, 12:49:58 AM »

Sorry if I post too many messages really curious abot this stuff.

but I've not yet been able to figure out what order of things matter along with iteration counts.  Like I really want to play mostly with bulbox/amazing boxes and such, but want to add formula's to change the structure and nature of the boxes to be more organic or strange.  But when I start to add other formula's I get the tic tac toe  formations.
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reesej2
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« Reply #1 on: August 04, 2011, 08:37:43 PM »

I'd like to help, but honestly I'm interested in this question myself. The issue is that by the nature of fractals, the behaviour is chaotic; so small changes to the iterating function can cause tremendous changes in the resulting image. What I would recommend is making the smallest changes you can; change the formula just a little, see if that changed the fractal in the general direction you want. If so, keep changing, tiny step by tiny step; otherwise, pick a new tiny change and try that instead.
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Madman
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« Reply #2 on: August 04, 2011, 10:00:21 PM »

You could try a negatively scaled mandelbox as the first formula and _rotate for the 2nd. Start with small (single digit) rotations at first.
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cKleinhuis
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« Reply #3 on: August 04, 2011, 10:17:52 PM »

ok, since i use this technique for more than 12 years, i got some insight into it....

first of all, try studying the effects of hybrids in the 2d view

second here are some forms of hybrids, that not all are available, but some forms are available:
i use some descriptions, in this cases formula1 always means standard mandelbrot

alternating - here a new formula is generated by f1(f2(...fn(z)) the result of the one formula is taken as input for the next formula, the effect on creating formulas in this way is that the "iteration bands" are the ones that show the behaviour of a certain formula, e.g. the first iteration is then formula1, for the second iteration ( so to say, the second band ) will then be the domain
of the second formula, and then first formula again takes over, for the alternating of many different formulas you need to increase the overall iteration count to really make use of it

it can not really be intuitive, but somehow effects seem natural, e.g. but it needs to be experimented with

follow ups - here formula1 is used for n iterations then formula2, this is quite easy to control, if formula1 is the mandelbrot, you just place another fractal inside the non-escaped points at that iteration this is quite cool

blending - in this hybrid form 2 formulas are blended over eachother, either by linear interpolating of the 2 values by a constant value ( e.g. 0.5 ) or by spherical/polar interpolating of the results of each formula, this is done for each iteration, when animating the blending value from 0 to 1 it is possible to "morph" virtually any fractal into any other fractal....

optional - in this method, any rule could be applied to differ between the formula to use, best work simple options like x>y, or abs(z)<1, this results in some "folding" operations, known from the barnsley fractal, or best actual example would be the mandelbox ( if constructed as hybrid from its parts )

so, if all would be written in tight mathematical style you would see that each hybrid can perform to a completely new fractal, but when interpreted visually you always will encounter similarities of each part of the generated formula

some hints and tips to try out

- alternating form this is the standard which is available in both renderers, just use 3 alternating formulas of exactly the same type, this would have the effect that it would look exactly like to choosen formula, but with tripled parameter set ... so, try animating wildly the properties of each, keeping in mind that you can easily transform it back to its original state by smooth transition, but it would not have to be a forward-backward animation, i mean the backward animation to its original state can be anything you like wink best viewd with 3 keyframes, the first to make an inital deformation, the second to force a different route to the starting point, and the 3rd keyfame for the original position, this would create a smooth loopable animation

so, this is what comes into my mind upon your question, report insights if you find some wink
and have fun exploring
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divide and conquer - iterate and rule - chaos is No random!
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