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Have fun playing with curvature

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Recently Tim Hutton and Adam Goucher have been playing around with hyperbolic tesselations. That has produced a {4,3,5} honeycomb grid for the reaction-diffusion simulator Ready, which Adam talked about on his blog a couple of days ago. Tim has also made a much simpler toy to play with in your browser: a visualisation of mirror tilings (the Wythoff construction) in spaces with different curvatures.

Hyperplay lets you select the kind of regular polygon you want to tile, and then your mouse controls the curvature of the space it sits in. Certain curvatures produce exact tilings of the space – for example, triangles tile a space with zero curvature – and you get projections of polyhedra for certain positive curvatures.

Aperiodical Round Up 6 – It glides to a stop as it reaches the end of the power stroke

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Hello. I’m Christian Perfect and it’s finally here: Aperiodical Round Up 6!

It’s certainly been a while since the last Round Up. You might not even have the words to describe just how long it’s been. Maybe the book Naming Infinity will help.

Newcastle MathsJam April 2012 Recap

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April’s MathsJam was very enjoyable. We did a bit of arts and crafts, a bit of playing games, and if it had been NBA Jam instead of Maths Jam I would have been entirely on fire because I used up all my IQ points solving some very fun puzzles. Durham were still on their Easter holidays so the attendance was a modest six people. That was just enough for everyone to be doing the same thing at the same time, so we had a good time.

Continue reading “Newcastle MathsJam April 2012 Recap” on cp’s mathem-o-blog

HyperRogue II – a roguelike on the hyperbolic plane

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I was directed to this game by a retweet by @haggismaths. It’s a roguelike (text-based explorey role-playing adventure game) which takes place on the hyperbolic plane. It’s a lot of fun. It’s hard to get your head round the fact that there’s a lot more stuff in between two lines in hyperbolic space than in Euclidean space, so it’s very hard to find your way back somewhere after it disappears over the horizon.

 

You can download a windows executable, or source code which will compile on Linux, at http://www.roguetemple.com/z/hyper.php

Conformal Models of Hyperbolic Geometry by Vladimir Bulatov

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Vladimir Bulatov makes art, including metal sculptures and jewellery, based on tilings of non-Euclidean spaces.

 

He has posted online some slides he made to go with a talk he gave at the JMM in 2010, about the many ways conformal mappings of the hyperbolic plane can produce interesting images. Quite a few of the diagrams are animated if you click on them, which I missed first time round.

There are a few other slideshows on similar topics on his site.

In addition to all that, Vladimir shares some very cool things on Google+.

Google+