RM=Raul Miller, DM=Devon McCormick Raul wrote: RM> I quite often will search for additional information when trying to solve > problems.
I'm with you. But it would be hard to look up details on the Dragon Curve if you didn't know the words "Dragon Curve". That's where I'm sitting now. Although I am obviously exploring other avenues of information. RM> Does it require the colors, or are they just a hint? Is the RM> fractal really solid? Or is that also just a hint? Perhaps RM> it's the vertices? Or does their sequence also matter -- RM> implying some kind of linear form? I think the colors and solidity are merely hints. Here's a much larger hint: http://en.wikipedia.org/wiki/Image:Dragon_curve_iterations_(2).svg For my own fractal, I do have access to a hint like this (though more limited; certainly no one drew the green arrows for me). RM> But, to take that any further, I need to understand which direction I should RM> be taking it. You got it. RM> Cliff Reiter has far, far more experience with fractals Ah! Why didn't I think of that? I have a copy of "Fractals, Visualization, and J". I just forgot about it. Thank you. DM> You really need to be able to access the output of a generating function to DM> have any chance at this but even then it might be impossible I should've been clearer about this. I do have access to the output of the generating function. Unlimited quantities, in fact; I'm constrained only by my patience. But let me clarify even further: I was trying to create one of these minimal prime generators that John brought up. I wrote a J verb that had something to do with primes, and while investigating ways to reduce it to a minimal prime generator, I discovered, to my surprise, that every prime is associated with a fractal in this context. Now I'm trying to reverse engineer the fractals to generate the primes. So I'm trying to find the generating functions for these fractals, without using the primes. Put another way, I'm trying to find out what these fractals "really are". I've solved the fractal for 2, and now I'm working on 3. It appears the fractals are themselves interrelated in a self-similar manner (the higher primes appear to be "zooms" of the lower primes). So I believe there is probably only one generating function, perhaps even parameterized by _1 p. prime . Since I've got the function for 2, I am trying to use that as a tool to crack 3. And there are tantalizing hints I might succeed. But then again, 2 and 3 have very different flavors (mountainous vs. castle-mountain hybrid), and 5 and beyond have a different flavor again (castleish, and it is within this set that I observe the "zooming" relationship). So maybe my quest for a single function is blinding me to a "simple way" to describe 3. But I don't think so; in fact, I think the zooming relationship is due to my paucity of data (owing to a lack of patience to generate more), and if I had an infinite data set, then I wouldn't have this "flavor discontinuity" between different prime fractals. DM> Have you looked at work by Barnsley et al. on iterated function systems? Nope, but I'll do so now. Thanks for the pointer! -Dan ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
