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A328074 Coordination sequence for a certain multiscale substitution tiling of the plane by squares.

%I A328074 #32 Mar 28 2020 10:12:32
%S A328074 1,12,16,16,40,52,96,84,72,92,128,104,68,104,112,148,168,140,136,248,
%T A328074 208,264,264,284,264,364,384,412,328,404,400,496,392,408,416,424,372,
%U A328074 408,456,468,468,504,540,576,572,616,608,616,576,616,556,576,620,612
%N A328074 Coordination sequence for a certain multiscale substitution tiling of the plane by squares.
%C A328074 This substitution rule dissects the unit square into a central square of side 3/5 and 16 surrounding squares of side 1/5.
%C A328074 What is the limiting shape of the contours (if it exists)?
%C A328074 From _Lars Blomberg_, Oct 18 2019: (Start)
%C A328074 Let s be the size of a square. The substitution rule is to replace it by one central square (size s*3/5) and sixteen smaller squares around it (size s*1/5).
%C A328074 Start with a single square as generation 0.
%C A328074 For each new generation first substitute the central square, let c be the size of the new central square.
%C A328074 Then substitute all non-central squares with size >= c. Repeat the last step if required. (End)
%H A328074 Lars Blomberg, <a href="/A328074/b328074.txt">Table of n, a(n) for n = 0..596</a>
%H A328074 Lars Blomberg, <a href="/A328074/a328074.png">Illustration of coordination sequence for generation 12</a>
%H A328074 Yotam Smilansky, <a href="https://vimeo.com/364312799">Patterns and Partitions</a>, Experimental Mathematics Seminar, Rutgers University, Oct 03 2019.
%H A328074 Yotam Smilansky, <a href="/A328074/a328074.pdf">Central portion of the tiling.</a>
%H A328074 Yotam Smilansky, <a href="/A328074/a328074_1.pdf">Colored picture of central portion of tiling showing contours.</a>
%H A328074 Yotam Smilansky, Yaar Solomon, <a href="https://arxiv.org/abs/2003.11735">Multiscale Substitution Tilings</a>, arXiv:2003.11735 [math.DS], 2020.
%K A328074 nonn
%O A328074 0,2
%A A328074 _N. J. A. Sloane_, Oct 07 2019, based on an email message from _Yotam Smilansky_
%E A328074 More terms from _Lars Blomberg_, Oct 18 2019