ZenoRogue | Heat transfer in a pentagonal tessellation @ZenoRogue | Uploaded December 2019 | Updated October 2024, 1 hour ago.
In each iteration, temperature of every cell is the average of temperatures of itself and its (five) neighbors in the previous iteration.
Thus, in the first iteration, the starting cell has temperature 1 and everything else has temperature 0; in the second iteration, the starting cell and all its neighbors have temperature 1/6; and so on.
The tessellation defines a distance which is different than the Euclidean norm -- if you examine what is the shape of the set of cells which can be reached in at most N steps, you get a polygon (here, a hexagon).
However, heat spreads in perfect Euclidean circles (on a sufficiently symmetric tiling), according to the Gaussian distribution. (It would be different for a tiling of the hyperbolic plane.)
Featuring the tessellation by Marjorie Rice, see: tandfonline.com/doi/full/10.1080/17513472.2018.1453740
Made with the HyperRogue engine.
In each iteration, temperature of every cell is the average of temperatures of itself and its (five) neighbors in the previous iteration.
Thus, in the first iteration, the starting cell has temperature 1 and everything else has temperature 0; in the second iteration, the starting cell and all its neighbors have temperature 1/6; and so on.
The tessellation defines a distance which is different than the Euclidean norm -- if you examine what is the shape of the set of cells which can be reached in at most N steps, you get a polygon (here, a hexagon).
However, heat spreads in perfect Euclidean circles (on a sufficiently symmetric tiling), according to the Gaussian distribution. (It would be different for a tiling of the hyperbolic plane.)
Featuring the tessellation by Marjorie Rice, see: tandfonline.com/doi/full/10.1080/17513472.2018.1453740
Made with the HyperRogue engine.
