update re Perron tiles
From
Stewart Robert Hinsley@21:1/5 to
All on Sun Sep 4 12:39:10 2016
I've updated the heuristics for Perron tiles to cover more completely
tiles associated with square and hexagonal grids. (I previously knew
that the heuristics for the general case were overrestrictive for those
groups of tiles, but hadn't articulated the specific, relaxed,
heuristics for those groups.)
www.stewart.hinsley.me.uk/Fractals/IFS/Tiles/Perron.php
The changes are
1) To restate the contraction/rotation element explicitly in term of
units, which are rational units (square roots of 1) in the general case, Gaussian units (4th roots of 1) in the case of a square grid, and
Eisenstein units (6th roots of 1) in the case of a hexagonal grid.
2) The coeffecients of the polynomial forming the vector element are extended from rational numbers to Gaussian rationals for a square grid,
and to "Eisenstein rationals" for a hexagonal grid.
--
SRH
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