Yet another continuum of rep-3-tiles, i.e., self-similarly trisectable 2D figures. Two others are parallelogram skewings of the sqrt 3 by 1 rectangle (first figure on balanced.htm) and the stretchings of "floppy fudgeflake" in continuum.htm. This time we have a countablegon rather than a frac-tile. The trisection is easy (harder if you don't know it's self-similar) and is left as an exercise.
(c2)
dispfun(all)$
(e2) bleg(a) := block([xaxis : false, yaxis : false, equalscale : true,
plotnum : 998],
eval(funmake('paramplot, append(args(sfloat(matrix([1, - sin(a)], [0,
cos(a)]))
. '(matrix([zag(t), (2 - (2/(sqrt(3)))) * t + 2 - sqrt(3), sqrt(3)],
[zag((t/(sqrt(3)))) * sqrt(3), - 1, (sqrt(3) - 1) * t + sqrt(3) - 2]))),
'([t, - 1, sqrt(3)])))))
(e3) zag(t) := (mode_declare(t, float), (t/(3.0^(abs(nummod( - logb(3.0, abs(t)), 1) - 0.5)))))
(c4)
compile(zag)$
load("c:\\rwg\\climax\\blegzag.lsp")$
D:\231alpha\Macsyma2\system\init.lsp being loaded.
D:\231alpha\Macsyma2\system\mfeexpninput.fas being loaded.
D:\231alpha\Macsyma2\library2\pltfuncs.fas being loaded.
(c5)
bleg(%pi/3)$
(c7)
bleg(-%pi/3)$