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[GIF] The Great Mystery

Posted 5 years ago

The Great Mystery

The image consists of multiple layers of circles in a hexagonal grid arrangement. The layer scaling factors are integer powers of the golden ratio. Seamless infinite zoom is achieved by gradually blending in / out the fine / large scale layers. Draw function draws a single animation frame:

v1 = {Cos[30 \[Degree]], Sin[30 \[Degree]]};
v2 = {Cos[90 \[Degree]], Sin[90 \[Degree]]};
n = 2;
g ={
       Circle[i v1 + j v2, 1/2],
       {i, -3 n, 3 n, 1/2}, {j, -3 n, 3 n, 1/2}
m = 2;
Draw[ds_] :=
         {Opacity[2/3 (m - Abs[i + ds])/m], 
         Scale[g, GoldenRatio^(i + ds), {0, 0}]}, 
         {i, -m, m}
       PlotRange -> {{-n, n}, {-n, n}},
       Background -> Black,
       ImageSize -> 800
POSTED BY: Peter Karpov
7 Replies
Posted 5 years ago

Hey! Thats amazing! Yeah the hexagon represents an elementary part of our nature, you can find it almost everywhere, in the eyes of bees, even on saturn (the 6th Planet) ^^ and in all what is elementary for life like carbon, here a example from a carbon molecule, recorded with a atomic force microscope (atomic/scanning force microscope, AFM) in the IBM research center in zurich.

enter image description here


Just for clarification: As it stands

 In[68]:= Grid[
 Join[{{"ds", "black", "white"}}, 
   Join[{Range[-5, 5]}, 
      ImageLevels /@ (Binarize /@ (Image /@ (Draw /@ 
             Range[-5, 5])))], {2}]]]]]

ds     black         white
-5     640000           0
-4     640000           0
-3     489362        150638
-2     458308        181692
-1     430486        209514
0      430486        209514
1      430486        209514
2      511558        128442
3      581104         58896
4      640000           0
5      640000           0

for Abs[ds] > 3 the graphics from Draw[ds] is uniformly black. An infinite zoom cannot be directly observed. The pictures for $ds \in \{-1,1,1\}$ seem to agree visually. How did $ds$ vary in the GIF animation?

Background: I'm interested in a working example of a fractal one can zoom out, with other words iterate backwards behind the starting set or with again other words having the starting set appearing if iterating from negative iteration numbers to iteration number 0. Then going forward, i.e. zoom in. Your example seemed to deliver it, but seems to need some more work to accomplish that.

POSTED BY: Udo Krause
Posted 5 years ago

Forgot to mention, ds varies from 0 to 1. It is the fractional part of the scale exponents, so when it reaches 1 we have the same set of scales and a perfect loop. If there was an infinite number of layers, we could change ds from -inf to +inf.

POSTED BY: Peter Karpov

enter image description here - Congratulations! This post is now a Staff Pick as distinguished by a badge on your profile! Thank you, keep it coming!

POSTED BY: Moderation Team
Posted 5 years ago

That looks amazing with that added. If you really want to make it look trippy, add some color to it. lol

POSTED BY: Edgard Murr

Mysterious stuff!

Your posted animated GIF consists of 60 single frames, according to my Australian file manager, file size being 14MB woah. File seems attached to forum. I had thought that file size attachment limitation was 10MB.

Never mind. Loving it too!

POSTED BY: Raspi Rascal
Posted 5 years ago

Love it, great job!

POSTED BY: Bryan Lettner
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