See Switching from management issues to Expert-Guru level sessions, we're taking in "Fractal Fun with Revit Repeaters and Adaptive Components." Tim Waldock is telling us how fractals are paterns that repeat themselves repeatedly, infinitily.
He created an adaptive component to try to recreate the Koch snowflake in Revit. In 2D it looks jsut kind of ok, with some irregularities, perhaps because some lines went 3D. He then tried a self-nesting triangle using intersecting tubes. See photograph below.
Next he tried semi-fractal trees using divided path. The trunk is a cylinder, with three branches and each branch having three more, limited to a sphere at the tips. But the process was very slow, so slow that it was nearly unusuable. He suggests Autodesk look at speeding up adaptive components, because otherwise people simply won't use it. See buildz.blogspot.com.au/2011/02/parametric-patterns-x-recursion.html
The nearest practical operation in Revit, he found, is nested repeater patterns. He looked for some examples in nature, and found fences with such patterns, and then worked at recreating them with adaptive components on paths -- using no mathematical formulae. He then figured out how to make the fence follow the varying elevations of a topo map -- with this catch: it works in Revit 2014 but not 2013, so Autodesk programmers have fixed some of the problems. See photograph below.
Now he is describing 2D nested repeater patterns, like dividing surfaces. He is showign all the kinds of things he tried, mostly with success and sometimes ending in errors. When there are no formulae, then performance is not too bad; as soon as formulae are added, performance slows right down. He has the step by step procedure in his handout notes.
Why bother? Well, this repeating pattern stuff is of great interest to curtain wall designers -- also adding holes, where structural steel might need to punch through the wall. But voids don't work wtih adaptive components, unless you use the new Cut with Voids function. "You might not find that it works in every area, and hopefully it will be fixed in due course."