That's neat. I spend my work days simulating advanced nuclear reactors that have hexagonal fuel assemblies. In my codes I've used a lot of this info. This is an excellent resource that I'll be referring people who come from the more traditional square lattice world.
Tangentially related, I have heard of modelling forest fires with cellular automata.<p><a href="http://en.wikipedia.org/wiki/Forest-fire_model" rel="nofollow">http://en.wikipedia.org/wiki/Forest-fire_model</a><p>The grid is usually rectangular, and I've always found this a bit odd: hexagons represent 2-d sphere packing, so they always seemed more natural to me. I once asked researchers in the field about this, around 2006, and they responded that rectangular grids serve just as well. I just found this paper from 2007 where apparently hexagonal grids fare better:<p><a href="http://www.sciencedirect.com/science/article/pii/S0307904X06000916" rel="nofollow">http://www.sciencedirect.com/science/article/pii/S0307904X06...</a><p>This makes me wonder, for realistic models that are meant to model a notion of neighbour cells, why aren't we always using hexagonal grids in 2d or higher-dimensional analogues? With rectangular grids, you're always faced with the choice of defining whether touching on edges and corners count as neighbours or not, which seems like an unnatural choice. Why, then, does this not seem to matter in the end?
Fascinating! One of Affirm's old job application puzzles was about a hexagonal grid. I did a write-up[1] of how I solved it, unaware that I was reinventing the wheel. The cube coordinates abstraction would have been <i>killer</i> for being able to explain things to myself.<p>[1]: <a href="http://vincentwoo.com/2013/03/08/above-and-beyond-the-affirm-job-puzzle/" rel="nofollow">http://vincentwoo.com/2013/03/08/above-and-beyond-the-affirm...</a>
This was a fantastic article -- examples were concise and clear, and everything was well-written.<p>Tangentially, I'd love to know the best way to create the visuals for this kind of content. I assume no one's writing all those SVGs by hand, right?
20 fun facts about hex grids:
<a href="http://gamasutra.com/blogs/HermanTulleken/20140912/225495/20_Fun_Grid_Facts_Hex_Grids.php" rel="nofollow">http://gamasutra.com/blogs/HermanTulleken/20140912/225495/20...</a>
I've never seen hex described this way, but here's how I envision simplifying their logic in games:<p>a regular 2d array, but with every-other row logically offset by 50% of the cells width, thus you end up with:<p><pre><code> [ ][ ][ ][ ][ ]
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</code></pre>
super simple data structure (normal 2d array), and pathfinding isn't difficult (use hex algos). I wonder why nobody ever writes about this....<p>Edit: ahh, the article kind-of describes this in the "Offset coordinates" section, just no explicit mention of able to use an array for storage.
I would like to see a game on a Penrose tiling. Obviously you couldn't make it wrap though.<p><a href="http://en.wikipedia.org/wiki/Penrose_tiling" rel="nofollow">http://en.wikipedia.org/wiki/Penrose_tiling</a>
That is an amazing resource and I used it when developing my hex game library for PixiJS.<p><a href="https://github.com/mark-harmon/HexPixiJs" rel="nofollow">https://github.com/mark-harmon/HexPixiJs</a>
I've explored similar questions using a grid of equilateral triangles. Obviously they are very close in spirit. I wonder though, if the triangles are somehow more basic.
I wonder what a non-cubic polyhedron-based voxel system would look like, without going all the way to marching cubes/tetrahedrons (where the cubes/tetrahedrons are only part of the algorithm that helps in rendering basically arbitrary voxels).<p>To wit: <a href="http://mathworld.wolfram.com/Space-FillingPolyhedron.html" rel="nofollow">http://mathworld.wolfram.com/Space-FillingPolyhedron.html</a>
If you want to get into grid programming, the MOAI framework has pretty good support, and the samples are pretty easy to grok: <a href="https://github.com/moai/moai-dev/blob/develop/samples/grid-hex/main.lua" rel="nofollow">https://github.com/moai/moai-dev/blob/develop/samples/grid-h...</a>
For anyone who hasn't read it, (and is interested ofc.) this website has one of the best explanations of A* I've ever read.<p><a href="http://www.redblobgames.com/pathfinding/a-star/introduction.html" rel="nofollow">http://www.redblobgames.com/pathfinding/a-star/introduction....</a>
Wow, I've been trying to make a Settlers of Catan game for fun and the thing I struggle most with is the board algorithms. This a fantastic resource to help with that, thanks.