Monthly Archives: January 2013

Graph minors

This is now, at the time of writing, the longest article on cp4space. We’ll begin with a very well-known problem, which asks whether it’s possible for three houses on the plane to be connected to three utility suppliers without crossings. What appear … Continue reading

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Alexandroff line

If this isn’t one of Ben Elliott and Hunter Spink’s bizarre mathematical objects of the week, it certainly deserves to be. This is a strange object which locally behaves like the real line, but is much longer. Instead of considering … Continue reading

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Generalised Truchet tiles

A long time ago, in a monastery far away, a monk called Sebastian Truchet decided to create patterns by tiling a square grid with a single type of tile (in two orientations). For instance, one possible pattern of 64 Truchet … Continue reading

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Cipher 11: Musical mayhem

This cipher again is separated into two parts, namely an audio file and the following ciphertext. ZKIGPWQ SLZSIIJ PBJRQKI TIMFTBE PEIVCNP CVHFEHA OAXINDB PTGDPUO PSJRBEP ZAAAAAA Unless you’re pitch perfect, you might also find this useful: I’ll leave you to work out … Continue reading

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Bombers and Basilisks

Tim Hutton has announced the release of Ready 0.5, which is now able to support cellular automata and reaction-diffusion systems on three-dimensional honeycombs. There are a few sample patterns on Penrose tilings as well. Replicators and Feynman diagrams On the subject … Continue reading

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The Ξ function

This is the final article on fast-growing functions. In the first two articles we looked at computable functions, up to and including Friedman’s TREE function. The third article described the Busy Beaver function, which eventually overtakes all computable functions. This … Continue reading

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Topological tacks

If you’ve bought a box of drawing pins from a stationery store, you’ll observe that the pins do not pack tightly at all, and there is lots of empty space in there. Indeed, it’s impossible to pack them particularly efficiently, … Continue reading

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Egmohedron

Partially inspired by the chiral icosahedral sculptures by George Hart and Bathsheba Grossman, I have decided to create one of my own. It’s composed of thirty identical components, each of which is a distorted lemniscate. Note that the lemniscate has … Continue reading

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Cipher 10: 2013

Assuming that this has been timed correctly, it should appear after the first minute of the first day of the new year. To celebrate this, today’s cipher is simply a matrix of 2013 binary digits. I’ll include this in both a … Continue reading

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