Lyapunov fractals

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Offline vasyan

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« Reply #150 on: March 04, 2019, 03:18:01 PM »
Graining is reduced and even destroyed by supersampling. ;)
I did not observe that Lyapunov algorithms work with numbers of the order of 1E+100 and higher. On the other hand, if you use a very large scale in the same way as it happens in the Mandelbrot fractals, then double precision may not be enough.

Offline ThunderboltPagoda

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« Reply #151 on: March 04, 2019, 07:12:32 PM »
This depends on the specific task.
For some cases, not only single/double/extended, but also the coprocessor flag.
See TFPUPrecisionMode and functions GetPrecisionMode/SetPrecisionMode in System.Math unit.
For example - rendering a Taylor fractal with different precision modes (see attachment).

Well, these are two quite different images. But my remark only refers to Lyapunov fractals, and in line with marcm200, I still think that the precision mode doesn't make so much difference here. It has an impact on the quality (graininess), but not on the overall structure of the image. And it's a compromise. Single precision allows me to use FastMath in my program, and that makes it 5 times faster. And that, in turn, allows me to render higher resolution images in acceptable time - which improves the quality. At the bottom line, there might even be a positive impact of FastMath on the image quality (given a somewhat restricted rendering time).

Offline vasyan

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« Reply #152 on: March 05, 2019, 02:19:48 AM »
Well, these are two quite different images. But my remark only refers to Lyapunov fractals, and in line with marcm200, I still think that the precision mode doesn't make so much difference here. It has an impact on the quality (graininess), but not on the overall structure of the image. And it's a compromise. Single precision allows me to use FastMath in my program, and that makes it 5 times faster. And that, in turn, allows me to render higher resolution images in acceptable time - which improves the quality. At the bottom line, there might even be a positive impact of FastMath on the image quality (given a somewhat restricted rendering time).
It is interesting to see the FastMath unit, it is very strange that single is 5 times faster than double.
For research of fractals with a very large scale, you cannot do without an extended type.

Offline ThunderboltPagoda

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« Reply #153 on: March 05, 2019, 11:46:05 AM »
It is interesting to see the FastMath unit, it is very strange that single is 5 times faster than double.

The speed increasement doesn't come from single vs. double. It comes from the TVector4 type, which makes use of the SSE2 units of modern CPUs. Using it, you can compute 4 pixels at once, instead of only one, and that gives a factor 4 in speed. The rest comes from faster functions like FastLog2.

Offline marcm200

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« Reply #154 on: March 07, 2019, 02:49:47 PM »
Thanks for the clarification. I searched for some similar library for C++ and found google's mathfu and some log/exp fast code. I am currently trying to incorporate that, together with some code snippets from the internet for approximation of sine. So far I couldn't find a log-function that works on the vector, so I might need to code that by some Taylor series approximation myself. But the fast exp/log and sine on just double-values gave a 2-fold speed increase! Especially for the 3D Lyapunov spaces I'm currently computing that helps a lot.

Offline vasyan

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« Reply #155 on: July 31, 2019, 10:11:36 AM »
However, I wanted to get an image of a Lyapunov fractal with the highest possible quality.
I tried to make a UFO fractal with a 10-x supersampling. Rendering each image took about 60 hours.
In the first embodiment, the initial value of X = 0.5. In the second variant, the initial value of X is zero.
Someone from the members of the forum asked about the different initial values of X - I propose to compare.
P.S. In the upper left corner is another UFO. ;)

Offline marcm200

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« Reply #156 on: July 31, 2019, 10:35:31 AM »
Rendering each image took about 60 hours. In the first embodiment, the initial value of X = 0.5. In the second variant, the initial value of X is zero. Someone from the members of the forum asked about the different initial values of X - I propose to compare.

60 hours per image - nicely done! I'm always concerned about power failure in such a long term, so I'm saving temporary data much too often, increasing the computation time even more.

As for the x0 value. I did a rough sweep when I started again with Lyapunov images last year, but did not encounter big differences (comparing some 2D images or calculating a stack of images changing x0 and looking at the 3D cube), so I take 0.5 as standard now and do not compute other values. But you're right, would be interesting to know when a change in the initial value has an advantage of some sort.


Offline pauldelbrot

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« Reply #157 on: July 31, 2019, 02:27:09 PM »
See what happens if you randomly pick x0 (uniform in [0,1]) for each sample, combined with 10x10 oversampling. Should make the artifacting go away and make the stalks in front of other stalks translucent.

Offline Dinkydau

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« Reply #158 on: August 02, 2019, 09:52:39 PM »
Beautiful and super weird render. I like it.

Offline ThunderboltPagoda

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« Reply #159 on: August 03, 2019, 04:24:43 PM »
Damaged UFO (no supersampling)

Offline vasyan

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« Reply #160 on: August 13, 2019, 12:15:41 PM »
P.S. In the upper left corner is another UFO. ;)
I tried to render this image fragment with 10x supersampling - another UFO. ;)


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