Talk:Iterated function system: Difference between revisions

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:The paper "fractals, graphs and fields" by Franklin Mendivil [http://mathdl.maa.org/mathDL/22/?pa=content&sa=viewDocument&nodeId=3128] explained the two methods and their equivalence very well. Recommended if there's others out there getting confused. :-) The construction paragraph seems correct, though it leaves out a lot of detail. [[User:EverGreg|EverGreg]] ([[User talk:EverGreg|talk]]) 19:40, 26 December 2009 (UTC)

to EverGreg:

"Method 2 as described here do effectively the same sequence of transformations but only plots the last point."

There's a subtlety in method 2. Note that it doesn't say "generate a sequence of transformations". It says "generate EACH POSSIBLE sequence of transformations" (implication: from a known starting point in space.)

If you have 3 transformations and you want sequences of length 10, you have 3^10 possible sequences of transformations. Given a common (arbitrary) starting point, this will yield 3^10 end points. Those 3^10 end points are plotted and make your fractal. [[Special:Contributions/46.64.181.38|46.64.181.38]] ([[User talk:46.64.181.38|talk]]) 14:11, 19 April 2014 (UTC)

::Right. Another way of looking at it is that the chaos-game algorithm is a random depth-first "search" that never backtracks, while Method 2 is an exhaustive search up to a given depth. But yes, this paragraph is super unclear. I just improved it slightly, but a '''lot''' more work is needed. [[User:Kragen|Kragen Javier Sitaker]] ([[User talk:Kragen|talk]]) 05:49, 19 July 2014 (UTC)

==Example==

Just not an encyclopedic, throught with ferns and triangles [http://vimeo.com/13074728 IFS animation 1] and [http://vimeo.com/12943444 IFS animation 2] <small><span class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Edo 555|Edo 555]] ([[User talk:Edo 555|talk]] • [[Special:Contributions/Edo 555|contribs]]) 14:05, 8 July 2010 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->

== Major missing topics ==

Although a few are mentioned as links, this page currently doesn't talk about any of these IFS topics, which I think are interesting and important:

* fractal image compression using IFSs;

* escape-time rendering of IFSs by inverting the functions;

* ray-traced rendering of 3-D IFSs;

* the relationship between IFSs and L-Systems, at any rate the commonly-studied L-Systems (it's easy to come up with a pathological L-System that doesn't obviously correspond to any IFS);

* Barnsley's deterministic iteration algorithm, which I guess is "Method 2"?

* the various other rendering methods presented by Hepting et al. 1991;

* the "collage theorem";

* Bell's "tesseral synecdoche algorithm";

* the "grayscale photo-copy algorithm" and its connection to the invariant measure of the IFS;

* the problem of computing the IFS's bounding box;

* the need to balance transform probabilities for stochastic ("chaos game") rendering (and the difficulty of doing so);

* computing sound upper and lower conservative bounds on the IFS's attractor;

* the phase transitions observed during continuous parameter variation.

Some random set of slides I ran across mentioned that you can get good ray-tracing results by approximating your surface normal as a weighted sum of the surface normals of the bounding spheres of the different subunits, which was part of what I was trying to figure out. I was disappointed to find that we haven't written a better article on this topic yet.

Thoughts on which of these are most important to cover? How to organize them?

[[User:Kragen|Kragen Javier Sitaker]] ([[User talk:Kragen|talk]]) 06:19, 19 July 2014 (UTC)

== Zooming ==

The article says that zooming in on an IFS fractal using the deterministic and random iteration algorithms is impractical.

This may not be the case, depending on how broadly you conceive each algorithm. I've been investigating producing high depth zooms, using a modification of the (depth first) deterministic iteration algorithm and reached a zoom of 5 × 10¹⁵⁰, using native 64 bit floating point arithmetic, without any noticeable deterioration in image quality, at little cost in extra computation time. At this point I hit an arithmetic overflow in the calculation of how deep the iterations should be, but this code can be refactored to avoid this. The modified code is ticking away and has reached a zoom 7 × 10¹⁹⁰. It may be possible to get to over 10⁶⁰⁰.

The modification is to combine a shallow depth first deterministic algorithm with a pruned breadth first deterministic algorithm (i.e. selecting only those branches in the deeper parts of the tree which lie within the zoom).

I haven't tried it yet, but combining a random iteration algorithm with the same pruned breadth first deterministic algorithm, should also work. [[User:Lavateraguy|Lavateraguy]] ([[User talk:Lavateraguy|talk]]) 16:48, 3 November 2016 (UTC)