The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A328074 Coordination sequence for a certain multiscale substitution tiling of the plane by squares. 3
 1, 12, 16, 16, 40, 52, 96, 84, 72, 92, 128, 104, 68, 104, 112, 148, 168, 140, 136, 248, 208, 264, 264, 284, 264, 364, 384, 412, 328, 404, 400, 496, 392, 408, 416, 424, 372, 408, 456, 468, 468, 504, 540, 576, 572, 616, 608, 616, 576, 616, 556, 576, 620, 612 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This substitution rule dissects the unit square into a central square of side 3/5 and 16 surrounding squares of side 1/5. What is the limiting shape of the contours (if it exists)? From Lars Blomberg, Oct 18 2019: (Start) 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). Start with a single square as generation 0. For each new generation first substitute the central square, let c be the size of the new central square. Then substitute all non-central squares with size >= c. Repeat the last step if required. (End) LINKS Lars Blomberg, Table of n, a(n) for n = 0..596 Lars Blomberg, Illustration of coordination sequence for generation 12 Yotam Smilansky, Patterns and Partitions, Experimental Mathematics Seminar, Rutgers University, Oct 03 2019. Yotam Smilansky, Central portion of the tiling. Yotam Smilansky, Colored picture of central portion of tiling showing contours. Yotam Smilansky, Yaar Solomon, Multiscale Substitution Tilings, arXiv:2003.11735 [math.DS], 2020. CROSSREFS Sequence in context: A135451 A175784 A143090 * A068394 A189685 A126763 Adjacent sequences:  A328071 A328072 A328073 * A328075 A328076 A328077 KEYWORD nonn AUTHOR N. J. A. Sloane, Oct 07 2019, based on an email message from Yotam Smilansky EXTENSIONS More terms from Lars Blomberg, Oct 18 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 28 13:18 EST 2020. Contains 338724 sequences. (Running on oeis4.)