Pinwheel fractual grasshopper

Is there an easy way to great this fractualisation in grasshopper using a standard tiling of a set triangle possibly to follow attractor points?

http://en.wikipedia.org/wiki/Pinwheel_tiling

Replies to This Discussion

Permalink Reply by peter fotiadis on March 11, 2015 at 11:05am

No, this is classic fractal thinking (meaning that you need code to do it). I have somewhere a C# script that does this. I'll post it as soon as I can find it.

Permalink Reply by Ryan Kings on March 11, 2015 at 1:32pm

Great, Thanks Peter.

Permalink Reply by peter fotiadis on March 11, 2015 at 2:44pm

Hmm ...

The thing found after inquiring 214,67 C# scripts with paranoid names like "The_Four_Horsemen_666_V3A".

Has some odd behavior occasionally, but nothing not fixable.

Allow me the opportunity to bring this into a 100% customer satisfaction guaranteed state (he he) by adding a myriad of conflicting options, Lists of start triangles, cats, dogs and some (trivial) divisions by zero.

more tomorrow

best, Peter

Permalink Reply by peter fotiadis on March 12, 2015 at 1:19pm

Well ... I had plans to add a million fractal "tri" division patterns to that one but due to "some" unpleasant "events" in my practice no time for boogie ... get only 6 and wait for the trad update (V4 , that is).

PS: Make a sketch with any imaginable "tri division pattern" and I'll add it as another mode.

best, Peter

Attachments:

Fractal_triangle_V3.gh, 304 KB

Permalink Reply by peter fotiadis on March 13, 2015 at 1:56am

Added a 2nd "stop" mode (that makes a BIG difference). Corrected some "minor" logic oops moments (now runs 0.00025% faster: big progress).

Recycle the old thingy: obsolete.

Attachments:

Fractal_triangle_V3A.gh, 310 KB

Permalink Reply by Ryan Kings on March 13, 2015 at 5:19am

Peter,

Thanks very much for this! Works great.

Is there a way so that each triangle has a strict ruling such as below:

[much like http://www.bcl.com.au/melbourne/images/kdpics/P1101469.jpg]

Conway Tessellation

I intend to use this as a façade system and cost implications would benefit from a isometric triangle subdivided into smaller ones based upon the same dimensions [to avoid custom panels].

Also the voids relate to the gene pools. Is there a way I can alter this to respond to attractor points for example. Also, can I create the tessellation from standard points or a surface [if that's even possible].

Sorry for my below par Grasshopper knowledge. Hope those events have calmed down.

Thanks again.

Ryan

Permalink Reply by peter fotiadis on March 13, 2015 at 5:55am

Hi Ryan,

"Below par" means nothing: never think that way > we all are amateurs the one way or the other. Besides this has nothing to do with GH components, it's classic recursive approach managed with code (i.e. something - a function [ or "Method"] - calls itself until some stop condition occurs). Using separate functions for the "patterns" (a modular approach, so to speak) means that you can actually do anything imaginable.

Thus: creating another "pattern" (i.e. the logic that samples points into the next recursion [or "generation" if I may use the term]) is exceptionally easy (if you speak the freaky language, he he). Here's for instance the "instructions" for one of the 6 modes provided (divide at middle) - I know that you are not speaking the language, but the logic is rather clear (I do hope, he he):

Voids (or Fulls) is all about what triad collections are sampled for the next recursion. Compare this (Full) mode ...... VS the other option (Void).

So , what all these freaky things mean?

Simple my friend: it's time for the V4, what else? (including "mapping" to any surface Lists).

more soon

Permalink Reply by peter fotiadis on March 13, 2015 at 6:08am

BTW: Until the mighty V4 I'll add ASAP 2 mode modes PWRyanFull, PWRyanVoid

Permalink Reply by peter fotiadis on March 13, 2015 at 8:14am

One minute job it took me 1 hour (due to some other @@$5 "events").

Read instructions about what is the newly added RyanMode (does a right triangle (90 degrees) where the one leg is half the other > meaning that for each recursion "group" we have 3 identical panels or five if the Full mode is used [but does this affects seriously the tile cost? I doubt it]...).

Attachments:

Fractal_triangle_V3B.gh, 319 KB

Permalink Reply by peter fotiadis on March 13, 2015 at 8:56am

In fact this (*) is exactly what the equivalent function did already ... but using "free" points instead points constrained in that 1:2 + 90 degrees thing.

(*) Get p3 > find closest at p1p2 (in Plan English: "project"), divide p2p3, divide the triangle height, divide the remaining thing > sample points into triads > send them to the big daddy ... blah blah

best, Peter

Permalink Reply by peter fotiadis on March 14, 2015 at 8:34am

So .. we arrive into V4 AND still no Lists (V5 is almost ready): read and enjoy.

BTW: I've made actually this C# for facades - long time ago - but other things happened and I've buried it alive until now.

This V4 can sense if you feed it with your points and uses these instead of the p1,p2,p3 (it's a prelude for V5 that uses DataTrees of points making any surface subdivision a reality). Do the following: sample a triad of your points (NOT internalized) and feed the C# . Then ... start dragging these Rhino points around (the C# responds accordingly). See any difference?

The topology:

Well, the whole fractal logic (in this case) is to have 3 pts on hand (call them p1,p2,p3 : red, green, blue) and then project the "right" one, say, p3 to the Line (p1,p2) > do this > do that ... blah blah.

But ... what p3? that's the 1M question: Here for instance the right p3 (blue) is (by accident) the 3rd point entered (it's obvious the "projection" recursive logic):

but if you drag around a bit the points : p3 is now different (C# does this by sorting synchronously the triangle angles per point VS points) Numbers are used to indicate that "swift" : (0 for the new p1, 1 for the new p2, 2 for the new p3... etc). Compare with the initial points (red = ex p1, green = ex p2 , blue = ex p3).

and again different:

The 1M question:

In fractal thinking the big thing is when to stop: I could obviously control that by a counter ... but here the requirement is the tile min size (within unpredictable amount of recursions) : this is what the stop logic used does.

The 1B question:

So ... implementing fractal logic (against DataTrees of points) to a parametric environment ... requires a lot of questions: because each time the size of the start triad varies ... whilst the stop condition is constant: meaning that with a little bit of "good" luck you can reach incredible high amount of tiles (computer out of memory > Adios Amigos).

Obviously I'm taking having all possibilities in mind and especially big projects > big facades > millions (or zillions) of tiles > Armageddon > ....

more soon

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