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Author Topic: Ultra Fractal 6 - Development News  (Read 1341 times)
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morbidorbits
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« on: April 28, 2016, 03:28:16 PM »

Frederik has provided me with some news about Ultra Fractal 6.

Q1:  Is Ultra Fractal still in development, and if so, are there plans to incorporate these fast perturbation zooming methods?

A1:  I've got good news for you. I'm quite excited about perturbation calculations myself and have already finished implementing it for Ultra Fractal 6. Just need to complete a couple of other things and am hoping to be ready to release it later this year.

Q2:  Any plans to implement the newest discoveries outlined in this document: http://www.superfractalthing.co.nf/sft_maths.pdf (Q2 posted by jabeck at Ultra Fractal Forums)

A2:  The next version of UF will have this feature as well, both for the built-in Mandelbrot and for your own formulas. It's already working for me and is indeed quite a magical speedup.

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cKleinhuis
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« Reply #1 on: April 28, 2016, 07:14:28 PM »

hehe, i heard that from frederik last year in san sebastian ( or was it 2 years by now ) and we have seen the pertubation method in action
in fact he is such a genious that you have one new formula area something like

pertubation: return some pertubation function

and the ultrafractal parser is doing the rest for you, so pertubation methods can be developed by many people then and testing them out straight from the formula parser inside uf, which is awesome, a speed increase by factor of 100 frederik said, its a bit slower than kalles implementation, but he has developed a glitch avoiding algorithm ( which i do hope is sharing with us, as i requested that kindly cheesy )

yeah, great news, but did he mention a release date ?!
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---

divide and conquer - iterate and rule - chaos is No random!
quaz0r
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« Reply #2 on: April 28, 2016, 07:30:10 PM »

i think the only "glitch avoiding algorithm" would be to address precision loss with greater precision during perturbation, instead of recomputing with the same precision using a different reference point.  i havent experimented with that yet, but i suspect it might not be worthwhile at lower depths but probably becomes worthwhile past a certain depth where the precision required by reference points becomes too costly.
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recursiveidentity
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« Reply #3 on: May 13, 2016, 04:05:05 PM »

Yeah that was me that asked... smiley I'm jabeck there...  I look forward to UF 6!
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Kalles Fraktaler
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« Reply #4 on: May 13, 2016, 09:06:08 PM »

I have reasons to doubt that UF6 would be able to take any formula and make perturbation of it.

Take the standard mandelbrot formula as example.
Set d as delta and c is the start point of delta, z is the reference and r is the start point of the reference:
Perturbation of the standard mandelbrot is (z+d)^2+(c+r) - (z^2+r) => 2*z*d + d^2 + c
As you can see, both z^2 and the start of the reference r are eliminated.
Since r is an high precision variable, which very probably is out of bounds for hardware datatypes, it is as important to be removed as the high power of z!

I received a formula, (z*r)^2-(z+r) which I didn't succeed render with perturbation.
You can try it yourself.
Replace z with z+d and r with r+c, then minus the original formula.
((z+d)*(r+c))^2-((z+d)+(r+c)) - ( (z*r)^2-(z+r) )

Enter the formula in http://quickmath.com/webMathematica3/quickmath/algebra/simplify/basic.jsp and you get the result:
2z^2rc+z^2c^2+2zdr^2+4zdrc+2zdc^2+d^2r^2+2d^2rc+d^2c^2−d−c
As you can see, r is still there, so it is not possible, sorry

So what can be done with perturbation is probably not much more than what stardust4ever already exploited and I implemented in KF...
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Kalles Fraktaler
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« Reply #5 on: May 17, 2016, 12:26:35 PM »

Bump
It would be nice if anyone could prove me wrong...
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Pauldelbrot
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pderbyshire2
« Reply #6 on: December 23, 2016, 10:34:30 PM »

Bump
It would be nice if anyone could prove me wrong...

For (zr)2 - (z + r) where r is a parameter like the c in the original, isn't d -> (2zr2 + dr2 - 1)d going to work to perturb it? Since the RHS is a product of d the precision needs ought to be the same as perturbing the original.
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claude
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« Reply #7 on: December 24, 2016, 02:44:47 AM »

I received a formula, (z*r)^2-(z+r) which I didn't succeed render with perturbation.

Not quite an answer you might hope for, but I think it's possible by affine conjugacy (equivalence of quadratic polynomials) with a change of coordinates z -> Az + B:

We can solve for the parameters by conjugating:(Az+B)2 + s = A((rz)2 - z - r) + B  gives A = r2, B = -1/2, s = -3/4 - r3

iterations of w -> w2 + s should now be equivalent to iterations of z -> (rz)2 - z - r, where w = A z + B; z = (w - B)/A.

Practically speaking, you would convert from the unusual polynomial to the standard polynomial, then iterate that, converting back to the unusual polynomial for escape tests to get the right iteration count.

Using perturbation has a slight issue of converting from delta-r in the image plane to delta-s in the calculation plane, but I think it's not too hard (just do this once-per-pixel calculation in high precision).

If any software does this kind of change of variables automatically, I'd be impressed.

* affine-conjugacy.frag (1.74 KB - downloaded 10 times.)
« Last Edit: December 24, 2016, 03:25:23 AM by claude, Reason: typo » Logged
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