Author: peterkagey
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An M.C. Escher-inspired poster
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I wanted an excuse to use Harvey Mudd’s large format printer, so I made a movie-sized (27″×40″) poster for my office based on the second term of OEIS sequence A368138(n): \(A368138(2) = 154\). The idea here is that you have a a collection of tiles like , which you can rotate and mirror; you then…
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Triangle Center Patterns
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I made a video that illustrates a particularly interesting “discrete state random dynamical system,” which was inspired by a Tweet (and a mistake) that I saw. First, be hypnotized by this video, which I recommend you watch in 4K, and then scroll down to read about the inspiration and the cool math going on under…
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How to Make Animated Math GIFs: LaTeX + TikZ
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The first animated GIF that I ever made was made with the LaTeX package TikZ and the command line utility ImageMagick. In this post, I’ll give a quick example of how to make a simple GIF that works by layering images with transparent backgrounds on top of each other repeatedly. TikZ code In our first…
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XOR Triangles
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In this post, I’ll explore the math behind one of my Twitter bots, @xorTriangles. This bot was inspired by the MathOverflow question “Number triangle,” asked by user DSM posted in May 2020. (I gave an overview of my Twitter bots @oeisTriangles in my post “Parity Bitmaps from the OEIS“. And if you want to build…
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Robot Walks
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I’ve gotten a lot of mathematical inspiration from Project Euler questions, but perhaps the question that has gotten me thinking the most is Project Euler Problem 208: Robot Walks. In this problem, a robot takes steps either to the right or the left, and at each step, it turns \(\frac 15\) of the way of…
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Pour Le Science and the anti-Sum-Product Problem
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In March 2021, I got an out-of-the-blue email from OEIS editor Michel Marcus which totally delighted me. He wrote: This afternoon I went to the library.And I was browsing “Pour La Science” the French version of the Scientific American.And here is what I saw. I like the mysterious tone. He included this photo of an…
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Zimin Words and Bifixes
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One of the earliest contributions to the On-Line Encyclopedia of Integer Sequences (OEIS) was a family sequences counting the number of words that begin (or don’t begin) with a palindrome: Let \(f_k(n)\) be the number of strings of length \(n\) over a \(k\)-letter alphabet that begin with a nontrivial palindrome” for various values of \(k\).…
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My Favorite Sequences: A263135
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This is the fourth in my installment of My Favorite Sequences. This post discusses sequence A263135 which counts penny-to-penny connections among \(n\) pennies on the vertices of a hexagonal grid. I published this sequence in October 2015 when I was thinking about hexagonal-grid analogs to the “Not Equal” grid. The square-grid analog of this sequence…
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My Favorite Sequences: “Not Equal” Grid
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This is the third installment in a recurring series, My Favorite Sequences. This post discusses OEIS sequence A278299, a sequence that took over two years to compute enough terms to add to the OEIS with confidence that it was distinct. This sequence is discussed in Problem #23 of my Open Problems Collection, which asks for…
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My Favorite Sequences: A289523
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This the second post in a recurring series, My Favorite Sequences. If you like this sort of thing, check out the Integer Sequence Review from The Aperiodical! A289523: Packing Circles of Increasing Area In July 2017, I added a mathematically-silly-but-visually-fun sequence, A289523. The sequence works like this: place a circle of area \(\pi\) centered at…