Kirby Urner wrote:

>In Fuller's synergetic geometry, circles don't become infinite lines, but

>just bigger and bigger circles. Lines that appear locally straight are just

>that: local. Clearly we're starting with different assumptions than those

>of Euclidean greek metaphysics. More from Democritus. Lines aren't

>perfectly straight either -- zoom in and they become zig-zaggy/wavilinear.

>Zoom out, and all you get are curves and great circles.

>

FWIW, I am working with (as in studying and implementing some tools in

PyGeo to enliven that study of) the geometry of complex numbers. And

doing so in such a way that all fundamental elements are defined by its

2X2 hermitian matrix. So I am getting fairly abstract - a "line" has

hermitian[0][0] == 0, else I am looking at a "point" or a "circle".

Drawing the damn things is a lot less abstract - and as hermitian[0][0]

approaches 0, a line makes a better represetantion - is all. And since

things are dynamic, I need my iinstances to think on their feet as to

what makes a better representation. If/else is really all I need - but

I was playing in my head with trying something more "dramatic".

Fredrk Lundh - the fbot and author of PIL - posted a blog entry a few

months ago about working with complex numbers to do basic image

manipulation. With Numeric in play, I can imagine a lot of efficiency

gains by working with it and the Python built_in complex numbers- via

Hermitian matrixes and 2X2 mobius transformation matrixes - to

accomplish a lot of the kind of image transformation effects that I

imagine are normally done otherwise. I expect that experimentation

along these lines is going to eventually get me more into playing with

bitmap graphics, whereas until now I have been a vector graphics kind of

guy.

Art

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