Brand New Method for True 3D Fractals.

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Offline gerrit

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« Reply #30 on: October 10, 2019, 02:51:33 AM »
Parameter space slice at z=0.2968.

Offline WAUthethird

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« Reply #31 on: October 17, 2019, 02:50:08 AM »
Dunno what you mean by "true". 3D escape-time fractals are essentially approximations anyways, and it's impossible to get a "true" 3D ES fractal, as has been said before. I suppose it does rely heavily on your personal definition of a true 3D ES fractal, but mathematically it is incorrect.

Offline TylerSmith

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« Reply #32 on: October 21, 2019, 02:17:42 PM »
Dunno what you mean by "true". 3D escape-time fractals are essentially approximations anyways, and it's impossible to get a "true" 3D ES fractal, as has been said before. I suppose it does rely heavily on your personal definition of a true 3D ES fractal, but mathematically it is incorrect.

Offline TylerSmith

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« Reply #33 on: October 21, 2019, 02:19:38 PM »
Dunno what you mean by "true". 3D escape-time fractals are essentially approximations anyways, and it's impossible to get a "true" 3D ES fractal, as has been said before. I suppose it does rely heavily on your personal definition of a true 3D ES fractal, but mathematically it is incorrect.

Offline TylerSmith

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« Reply #34 on: October 21, 2019, 02:22:51 PM »
I am saying it makes a 3D shape that occupies 3 dimensional space and has infinite detail along the x,y and z axis without being distorted. No additional calculations being thrown into the mix. And it does work. Did you look at any of the images? It totally works lol.

Dunno what you mean by "true". 3D escape-time fractals are essentially approximations anyways, and it's impossible to get a "true" 3D ES fractal, as has been said before. I suppose it does rely heavily on your personal definition of a true 3D ES fractal, but mathematically it is incorrect.

Offline WAUthethird

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« Reply #35 on: October 21, 2019, 11:32:25 PM »
I am saying it makes a 3D shape that occupies 3 dimensional space and has infinite detail along the x,y and z axis without being distorted. No additional calculations being thrown into the mix. And it does work. Did you look at any of the images? It totally works lol.

I can see that. Approximations can indeed be rotated. I have no objections to the fact that it is in 3 dimensions. This is nothing new.

Offline claude

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« Reply #36 on: October 22, 2019, 12:02:33 AM »
This is nothing new.

The interleaving of two 2D (x,y) and (y,z) iterations to make a 3D (x,y,z) fractal seems new to me.

Offline WAUthethird

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« Reply #37 on: October 22, 2019, 12:27:27 AM »
The interleaving of two 2D (x,y) and (y,z) iterations to make a 3D (x,y,z) fractal seems new to me.

That's true. I've seen maybe two examples of this being done before.

Offline marcm200

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« Reply #38 on: October 22, 2019, 09:01:47 AM »
I am saying it makes a 3D shape that occupies 3 dimensional space and has infinite detail along the x,y and z axis without being distorted. No additional calculations being thrown into the mix.
There is one additional algorithmical type of calculation: splitting the output of the first complex multiplication into real and imaginary part and using the latter for the 2nd multiplication. As this is done in every iteration, that sets it conceptionally apart from being just z▓+c in a sequential manner.

The approach produces a vast variety of Julia set shapes, something I've never encountered in the self-created tircomplex formulas I experimented with (they were all pretty dull in that regard).

Below is an example that even possesses an attracting period-2 cycle (turquois). It looks like a pair of walls where strangely shaped ping pong balls bounce off in between (yellow, non-immediate basin of attraction).

C={-37224616,8912896,12845056} * 2^-25, computed using the cell mapping/IA algorithm by Figueiredo et al.,
every pixel shows the identical bounded fate of a voxel of side length 2^-9.

Offline FractalDave

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« Reply #39 on: October 24, 2019, 11:40:39 AM »
There is one additional algorithmical type of calculation: splitting the output of the first complex multiplication into real and imaginary part and using the latter for the 2nd multiplication.

:)

ttps://fractalforums.org/fractal-mathematics-and-new-theories/28/ok-i-found-it-at-least-for-4d-anyway/3095/msg17348#msg17348

Also it does appear to have been done before - just not really noticed ;)

As to "True 3D" I guess from a fractal point of view the object should be fractal at any point on the surface in any direction, plus for true3D as oppossed to 4D etc. the math should not involve any more than 3 dimemnsions at any stage in the calculations. The Polar Complex method can be used like that as I say in the above post at the end i.e. only treat one of the first complex magnitude pair as a magnitude to apply to just one unit vector rather than using both, I just prefer the version where both are used which of course is always mathematically 4D.
In addition in a more aesthetic  context the x-y and x-z slices really ought to both be the same and both symmetrical around x, there should be small "brocolli" bulbs along both the y and z joining a main rotated cardioid and similarly fior all the bulbs connected to the main secondary on the spike....I did see a website once with this picture shown but I can no longer find it and have no idea how the image was created......if anyone knows where it is or finds it I'd love to know....it was in green with a reflection below if I recall correctly !!

BTW see my gallery on here for related renders using the Polar Complex....
« Last Edit: October 24, 2019, 12:36:22 PM by FractalDave »
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Offline FractalDave

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« Reply #40 on: October 24, 2019, 12:11:52 PM »
Just a reminder regarding "True 3D" stuff...newbies to this should start here: ;)

http://www.fractalforums.com/3d-fractal-generation/true-3d-mandlebrot-type-fractal/30/?PHPSESSID=1534a540b87477053da1e30b6fa824ac


and here:


http://www.fractalforums.com/the-3d-mandelbulb/truerer-true-3d-mandelbrot-fractal-(search-for-the-holy-grail-continues)/

Plus, on the "holy grail":

http://www.fractalforums.com/new-theories-and-research/how-to-recognize-the-holy-grail-fractal/

There's a whole lot more on the old fractalforums site too.
The "holy grail" has been looked for, for a long time - look up say "Rudy Rucker" ;)
« Last Edit: October 24, 2019, 12:34:49 PM by FractalDave »

Offline TylerSmith

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« Reply #41 on: November 07, 2019, 12:58:52 PM »
When and where lol

That's true. I've seen maybe two examples of this being done before.

Offline TylerSmith

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« Reply #42 on: November 07, 2019, 01:00:00 PM »
Well then I guess I found the holy grail.

Just a reminder regarding "True 3D" stuff...newbies to this should start here: ;)

http://www.fractalforums.com/3d-fractal-generation/true-3d-mandlebrot-type-fractal/30/?PHPSESSID=1534a540b87477053da1e30b6fa824ac


and here:


http://www.fractalforums.com/the-3d-mandelbulb/truerer-true-3d-mandelbrot-fractal-(search-for-the-holy-grail-continues)/

Plus, on the "holy grail":

http://www.fractalforums.com/new-theories-and-research/how-to-recognize-the-holy-grail-fractal/

There's a whole lot more on the old fractalforums site too.
The "holy grail" has been looked for, for a long time - look up say "Rudy Rucker" ;)

Offline TylerSmith

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« Reply #43 on: November 07, 2019, 01:01:41 PM »
You are correct. I meant it's using straight xyz coordinates as input and not using polar coordinates or spherical transformations etc.

There is one additional algorithmical type of calculation: splitting the output of the first complex multiplication into real and imaginary part and using the latter for the 2nd multiplication. As this is done in every iteration, that sets it conceptionally apart from being just z▓+c in a sequential manner.

The approach produces a vast variety of Julia set shapes, something I've never encountered in the self-created tircomplex formulas I experimented with (they were all pretty dull in that regard).

Below is an example that even possesses an attracting period-2 cycle (turquois). It looks like a pair of walls where strangely shaped ping pong balls bounce off in between (yellow, non-immediate basin of attraction).

C={-37224616,8912896,12845056} * 2^-25, computed using the cell mapping/IA algorithm by Figueiredo et al.,
every pixel shows the identical bounded fate of a voxel of side length 2^-9.

Offline TylerSmith

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« Reply #44 on: November 24, 2019, 03:01:36 PM »
I'm NOT USING THENPOLAR COMPLEX I was saying it does NOT use it.

Go to page one and read what I wrote please. This is rediculous.

:)

ttps://fractalforums.org/fractal-mathematics-and-new-theories/28/ok-i-found-it-at-least-for-4d-anyway/3095/msg17348#msg17348

Also it does appear to have been done before - just not really noticed ;)

As to "True 3D" I guess from a fractal point of view the object should be fractal at any point on the surface in any direction, plus for true3D as oppossed to 4D etc. the math should not involve any more than 3 dimemnsions at any stage in the calculations. The Polar Complex method can be used like that as I say in the above post at the end i.e. only treat one of the first complex magnitude pair as a magnitude to apply to just one unit vector rather than using both, I just prefer the version where both are used which of course is always mathematically 4D.
In addition in a more aesthetic  context the x-y and x-z slices really ought to both be the same and both symmetrical around x, there should be small "brocolli" bulbs along both the y and z joining a main rotated cardioid and similarly fior all the bulbs connected to the main secondary on the spike....I did see a website once with this picture shown but I can no longer find it and have no idea how the image was created......if anyone knows where it is or finds it I'd love to know....it was in green with a reflection below if I recall correctly !!

BTW see my gallery on here for related renders using the Polar Complex....


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