Peter Kagey

Tag: Art

  • Triangle Center Patterns

    Triangle Center Patterns

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    peterkagey

    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

    How to Make Animated Math GIFs: LaTeX + TikZ

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    peterkagey

    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

    XOR Triangles

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    peterkagey

    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

    Robot Walks

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    peterkagey

    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…

  • Parity Bitmaps from the OEIS

    Parity Bitmaps from the OEIS

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    by

    peterkagey

    My friend Alec Jones and I wrote a Python script that takes a two-dimensional sequence in the On-Line Encyclopedia of Integer Sequences and uses it to create a one-bit-per-pixel (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.…

  • Regular Truchet Tilings

    Regular Truchet Tilings

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    by

    peterkagey

    I recently made my first piece of math art for my apartment: a 30″×40″ canvas print based on putting Truchet tiles on the truncated trihexagonal tiling. I first became interested in these sorts of patterns after my former colleague Shane sent me a YouTube video of the one-line Commodore 64 BASIC program: 10 PRINT CHR$(205.5+RND(1));…