3D IFS
From Ultrafractal Wiki
also see:
David Makin's 3D IFS guide: [1], 3D IFS examples IFS
Hi all,
I just updated the 3D IFS formula in mmf4.ufm - it's still fully UF4 compatible.
I've changed the transformation view so that if "Transformation View" is set to "All" but "Show Transforms" is set to a particular transform then only the transform selected in "Show Transforms" is shown in its own colour, the rest are drawn in the base colour.
More importantly I've added "Restrict Consecutive Uses" and "Restrict Total Uses" on the transforms. These options (especially the first) for example allow use of transforms to produce rotations of your fractal where the rotating transform has scales at 100%. They open up yet more ways of controlling the IFS, especially when combined with the RIFS and depth restriction options.
For instance a version of this fractal by Garth Thornton (Xenodream): [2]
Can now be created in UF :) Note that exporting such a fractal from Xeno to UF won't work perfectly at the moment, some of the changes need to be done "by hand" - please contact me off-list if you want help on this.
Apparently there may be some issues with updating from within UF4 at the moment so to get the update to mmf4.ufm you may need to do so "by hand" from http://formulas.ultrafractal.com/ rather than getting it by updating within UF4.
bye Dave
Hi again,
For those who want to know more about how IFS works, here's an example to play with.
The attached UPR (the Sierpinski Tetrahedron) has the "Max. depth" parameter set to 1. This means that the image produced is only from the first depth of the IFS tree and the result is one spheroid per active transformation, in this case 4 spheroids. Each spheroid is a reduced scale copy of an imaginary original. If you modify the "Max. depth" parameter to 2 then the image from depth 2 of the IFS will be rendered. Here each of the 1st four spheroids is replaced by a reduced-scale copy of the whole from depth 1. Similarly if you continue to increase the max depth in units of 1 at each stage all the spheroids will be replaced by reduced size copies of the whole object from the previous depth. You can try the same thing on the default Menger Sponge that the 3D IFS formula produces.
That's fairly straightforward and obvious since the Sierpinski Tetrahedron and Menger Sponge only use scaling and translation in their transforms. Things get considerably more difficult to visualise when the transforms include rotations, skews etc. but the same principle with increasing depth in the IFS tree applies, with each depth increase each copy (spheroid) is replaced by a transformed copy of the whole object from the previous depth.
bye Dave
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Hi Dave,
What an awesome creature! But I would like to know: When you change a number in the almost endless list in the formula, do you know what you are changing? I don't. Here and there I change a number, sometimes nothing happens. Mostly it will change unpredictably. Is there a tutorial somewhere on the Internet to give me some clues? I am very impressed, and would like to understand the entire formula.
Regards,
Gerritjan Roubos
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Hi,
On the Sierpinski Tetrahedron example with "Max. depth" set to 1 try changing say "X rotation" on Transformation #2 to 45 (degrres), then increase the max depth in units of 1 looking at the render each time. What heppens here is that with Max. depth at 1 the rotation just moves the sphere belonging to Transformation #2 a little (bottom-left) but when you change the max depth to 2 there's a more noticeable change from the unrotated version because the sphere at depth 1 belonging to transform 1 is replaced at depth 2 by a scaled *and* rotated copy of the whole object from depth 1. Further rotations occur as you increase the depth for all applications of transform 1.
bye Dave
Copyright © 2007 by David Makin
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Hi Gerritjan,
I haven't done a tutorial one how IFS works because I simply haven't the time to do that :) Basically each IFS is made up of two or more combined transforms. Each transform is made up of scale values, rotations, skews and translations and it is these values that control the appearance of the IFS. I have done a very brief tutorial on the rest of the formula here: David Makin's 3D IFS guide
I've attached a version of "Flotsam" that has two layers, the top layer (the visible one) shows you how you can view the transforms that make up the fractal - if you "explore" the transform parameters on the active transforms in the layer showing the transformation view, you'll be able to see what the transforms you are controlling actually look like - and you can toggle the view back to the fractal image using the "View" parameter. Note that in the transformation view the big cube is what an untransformed cube looks like and the other smaller cubes are what the transformed cubes that produce the fractal look like.
bye Dave
Copyright © 2007 by David Makin
Hi,
Here's a better render of "Flotsam", I've just changed the lighting parameters slightly - rotated the remote light a little and modified the overall light strength and the strength of the camera light.
bye Dave
Copyright © 2007 by David Makin
