Category: Uncategorized

An M.C. Escherinspired poster
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I wanted an excuse to use Harvey Mudd’s large format printer, so I made a moviesized (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…

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…

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…

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…

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…

Pour Le Science and the antiSumProduct Problem
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In March 2021, I got an outoftheblue 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…

Zimin Words and Bifixes
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One of the earliest contributions to the OnLine 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 \(k\).…

Richard Guy’s Partition Sequence
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Neil Sloane is the founder of the OnLine Encyclopedia of Integer Sequences (OEIS). Every year or so, he gives a talk at Rutgers in which he discusses some of his favorite recent sequences. In 2017, he spent some time talking about a 1971 letter that he got from Richard Guy, and some questions that went…

Polytopes with Lattice Coordinates
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Problems 21, 66, and 116 in my Open Problem Collection concern polytopes with lattice coordinates—that is, polygons, polyhedra, or higherdimensional analogs with vertices the square or triangular grids. (In higher dimensions, I’m most interested in the \(n\)dimensional integer lattice and the \(n\)simplex honeycomb). This was largely inspired by one of my favorite mathematical facts: given…

Parity Bitmaps from the OEIS
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My friend Alec Jones and I wrote a Python script that takes a twodimensional sequence in the OnLine Encyclopedia of Integer Sequences and uses it to create a onebitperpixel (1BPP) “parity bitmaps“. The program is simple: it colors a given pixel is black or white depending on whether the corresponding value is even or odd.…