new tessellation samples

tessellations/README.txt

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+go to https://github.com/zenorogue/tes-catalog for more!

tessellations/affine/affine-fathauer-1-1-1.tes

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+## Fathauer triangle spiral, family 1, m=1, n=3
+a2.
+angleunit(deg)
+let(fi = (1+sqrt(5))/2)
+let(one = test(1/fi + 1/fi^2))
+tile(1,36,fi,36,1/fi,180,1/fi^2,108)
+conway("(0 2)(1 3)")

tessellations/affine/affine-square.tes

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+## square grid with affine transformations
+a2.
+angleunit(deg)
+tile(1,90,1,90,1,90,1,90)
+conway("[0 2](1 3)")
+# in the direction '0-2', stretch them by 1% and shear them by 50% (note that the direction is mirrored)
+stretch_shear(1.5, 0.5, 0, 0)

tessellations/affine/golden-spiral.tes

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+## Golden Spiral as an affine tessellation
+a2.
+angleunit(deg)
+let(fi = (1+sqrt(5))/2)
+let(one = test(1/fi + 1/fi^3 + 1/fi^4))
+tile(1,90,1,90,1,90,1/fi,180,1/fi^4,180,1/fi^3,90)
+conway("(0 3)(1 4)(2 5)")

tessellations/sample/brickwork.tes

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+## brickwork
+## a simple test
+e2.
+angleunit(deg)
+# 1's are edge lengths, and 0s and 90s are external angles, given in angleunits (i.e. degrees)
+tile(1,180,1,90,1,90,1,180,1,90,1,90)
+# consecutive edges in 'tile' description are numbered: 0, 1, 2, 3, 4, 5
+# consecutive tile types are numbered: 0, 1, 2, ... (here there is just one type)
+# the last 0 means that there is no mirroring
+c(0,0,0,3,0)
+c(0,1,0,4,0)
+c(0,2,0,5,0)

tessellations/sample/circlelimit3.tes

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+## Escher's Circle Limit III
+## Instructions:
+## load this;
+## load Escher's Circle Limit III in the texture mode;
+## "scale/rotate the texture" until centers of octagons coincide with center of Escher's squares;
+## you may "select master triangles" and pick triangles closer to the center;
+## enable the texture
+
+h2.
+angleunit(2*pi/3)
+distunit(edge(8,3))
+
+unittile(1,1,1,1,1,1,1,1) # YG
+unittile(1,1,1,1,1,1,1,1) # YB
+unittile(1,1,1,1,1,1,1,1) # YR
+unittile(1,1,1,1,1,1,1,1) # RG
+unittile(1,1,1,1,1,1,1,1) # RB
+unittile(1,1,1,1,1,1,1,1) # GB
+
+c(0,0,3,1,0)
+c(0,1,5,2,0)
+c(0,2,1,3,0)
+c(0,3,2,2,0)
+c(1,0,5,1,0)
+c(1,1,4,0,0)
+c(1,2,2,3,0)
+c(2,0,4,3,0)
+c(2,1,3,2,0)
+c(3,0,5,3,0)
+c(3,3,4,2,0)
+c(4,1,5,0,0)
+
+c(0,4,3,5,0)
+c(0,5,5,6,0)
+c(0,6,1,7,0)
+c(0,7,2,6,0)
+c(1,4,5,5,0)
+c(1,5,4,4,0)
+c(1,6,2,7,0)
+c(2,4,4,7,0)
+c(2,5,3,6,0)
+c(3,4,5,7,0)
+c(3,7,4,6,0)
+c(4,5,5,4,0)
+
+# these lines repeat connections from (0123) to (4567), and also tell the texture mode that four triangles should be repeated twice
+# (put them after specifying connections); however, it works better without them
+
+# repeat(0, 2)
+# repeat(1, 2)
+# repeat(2, 2)
+# repeat(3, 2)
+# repeat(4, 2)
+# repeat(5, 2)

tessellations/sample/circlelimit3b.tes

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+## Escher's Circle Limit III, mapped to {12,3}
+## After mapping circlelimit3.tes, change the tes file to this one
+
+h2.
+angleunit(2*pi/3)
+distunit(edge(12,3))
+
+unittile(1,1,1,1,1,1,1,1,1,1,1,1) # YG
+unittile(1,1,1,1,1,1,1,1,1,1,1,1) # YB
+unittile(1,1,1,1,1,1,1,1,1,1,1,1) # YR
+unittile(1,1,1,1,1,1,1,1,1,1,1,1) # RG
+unittile(1,1,1,1,1,1,1,1,1,1,1,1) # RB
+unittile(1,1,1,1,1,1,1,1,1,1,1,1) # GB
+
+c(0,0,3,1,0)
+c(0,1,5,2,0)
+c(0,2,1,3,0)
+c(0,3,2,2,0)
+c(1,0,5,1,0)
+c(1,1,4,0,0)
+c(1,2,2,3,0)
+c(2,0,4,3,0)
+c(2,1,3,2,0)
+c(3,0,5,3,0)
+c(3,3,4,2,0)
+c(4,1,5,0,0)
+
+c(0,4,3,5,0)
+c(0,5,5,6,0)
+c(0,6,1,7,0)
+c(0,7,2,6,0)
+c(1,4,5,5,0)
+c(1,5,4,4,0)
+c(1,6,2,7,0)
+c(2,4,4,7,0)
+c(2,5,3,6,0)
+c(3,4,5,7,0)
+c(3,7,4,6,0)
+c(4,5,5,4,0)
+
+c(0,8,3,9,0)
+c(0,9,5,10,0)
+c(0,10,1,11,0)
+c(0,11,2,10,0)
+c(1,8,5,9,0)
+c(1,9,4,8,0)
+c(1,10,2,11,0)
+c(2,8,4,11,0)
+c(2,9,3,10,0)
+c(3,8,5,11,0)
+c(3,11,4,10,0)
+c(4,9,5,8,0)
+
+# these lines repeat connections from (0123) to (4567), and also tell the texture mode that four triangles should be repeated twice
+# (put them after specifying connections); however, it works better without them
+
+# repeat(0, 2)
+# repeat(1, 2)
+# repeat(2, 2)
+# repeat(3, 2)
+# repeat(4, 2)
+# repeat(5, 2)

tessellations/sample/circlelimit3c.tes

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+## Escher's Circle Limit III, mapped to sphere
+## After mapping circlelimit3.tes, change the tes file to this one
+
+s2.
+angleunit(2*pi/3)
+distunit(1)
+distunit(edge(4,3))
+
+unittile(1,1,1,1) # YG
+unittile(1,1,1,1) # YB
+unittile(1,1,1,1) # YR
+unittile(1,1,1,1) # RG
+unittile(1,1,1,1) # RB
+unittile(1,1,1,1) # GB
+
+c(0,0,3,1,0)
+c(0,1,5,2,0)
+c(0,2,1,3,0)
+c(0,3,2,2,0)
+c(1,0,5,1,0)
+c(1,1,4,0,0)
+c(1,2,2,3,0)
+c(2,0,4,3,0)
+c(2,1,3,2,0)
+c(3,0,5,3,0)
+c(3,3,4,2,0)
+c(4,1,5,0,0)
+

tessellations/sample/floret.tes

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+## floret-like tiling
+## from Marek14's post in HyperRogue discord
+e2.
+angleunit(deg)
+tile(1,60,3,120,1,120,1,60,1,240,1,180,1,120)
+c(0,0,0,6,0)
+c(0,1,0,1,0)
+c(0,2,0,5,0)
+c(0,3,0,4,0)

tessellations/sample/hexiamond.tes

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+## {3,7} hexiamond
+h2.
+angleunit(2*pi/7)
+distunit(edge(3,7))
+unittile(1,3,1,4,1,3,1,4)
+conway("(0 1)(2 3)(4 5)(6 7)")
+sublines(1)
+# warning: this one is "nonorientable"

tessellations/sample/hr-standard-tiling.tes

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+## HyperRogue standard tiling
+h2.
+
+# we compute the edge length of the Archimedean tessellation we are using
+distunit(arcmedge(6,6,7))
+# note: subsequent results of arcmedge are given in terms of distunit
+
+# regangle(A,B) returns the internal angle of a B-gon with sidelength A
+
+let(u6 = regangle(1, 6))
+let(u7 = regangle(1, 7))
+
+unittile(u6,u6,u6,u6,u6,u6)
+unittile(u7,u7,u7,u7,u7,u7,u7)
+
+c(0,0,0,0,0)
+c(0,2,0,2,0)
+c(0,4,0,4,0)
+c(0,1,1,0,0)
+c(0,3,1,1,0)
+c(0,5,1,2,0)
+c(0,1,1,3,0)
+c(0,3,1,4,0)
+c(0,5,1,5,0)
+c(0,1,1,6,0)
+

tessellations/sample/marek313.tes

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+## {3,13} pentiamond 
+## from Marek14's post in HyperRogue discord
+h2.
+angleunit(2*pi/13)
+distunit(edge(3,13))
+tile(1,2,1,3,1,2,1,1,1,3,1,3,1,1)
+c(0,0,0,6,0)
+c(0,1,0,1,0)
+c(0,2,0,2,0)
+c(0,3,0,4,0)
+c(0,5,0,5,0)

tessellations/sample/marjorie-rice.tes

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+## Marjorie Rice tiling
+## see: "Marjorie Rice and the MAA tiling", Doris Schattschneider
+e2.
+angleunit(deg)
+let(u=sqrt(3)/3)
+tile(1, 150, u, 120, u, 90, 1, 120, 1, 60)
+tile(1, 150, u, 120, u, 90, 1, 120, 1, 60)
+tile(1, 150, u, 120, u, 90, 1, 120, 1, 60)
+
+#c(0,0,0,4,0)
+#c(0,3,2,3,0)
+#c(0,1,2,2,0)
+#c(0,2,1,1,0)
+#c(2,1,1,2,0)
+#c(1,0,2,4,0)
+#c(2,0,2,0,0)
+#c(1,3,1,4,0)
+
+# in Conway notation, tile #k can be identified with k primes or with @k
+conway("(0 4)(3 3'')(1 2'')(2 1')(1'' 2')(0' 4'')(0'')(3' 4')")
+
+# affect Vineyard/Zebra/Land of Power
+line(0)
+# heptagon role (affects e.g. Graveyard)
+grave(1)
+
+# draw sublines in the grid, for every pair of vertices in distance of 1 distunit
+sublines(1)

tessellations/sample/sliders.tes

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+## triangle alpha-beta-gamma, where alpha+beta+gamma = 120 degrees
+##
+## You can change alpha, beta, and gamma using 'tessellation sliders' in the geometry experiments menu.
+##
+h2.
+angleunit(deg)
+
+slider(a,40,0,120)
+slider(b,40,0,120)
+
+let(c = 120-a-b)
+
+let(ea=edge_angles(a,b,c))
+let(eb=edge_angles(b,c,a))
+let(ec=edge_angles(c,a,b))
+
+tile(ea, b, ec, a, eb, c)
+conway("(0)(1)(2)")
+
+cscale(.75)

tessellations/sample/sliders2.tes

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+## triangle alpha-beta-gamma, where alpha+beta+gamma = 120 degrees
+##
+## You can change alpha, beta, and gamma using 'tessellation sliders' in the geometry experiments menu.
+##
+## You can choose all three angles. Sliders are not allowed to change the structure of the map,
+## so if they do not add up to 120 degrees, they will not match.
+##
+h2.
+angleunit(deg)
+
+slider(a,40,0,120)
+slider(b,40,0,120)
+slider(c,40,0,120)
+
+let(ea=edge_angles(a,b,c))
+let(eb=edge_angles(b,c,a))
+let(ec=edge_angles(c,a,b))
+
+tile(ea, b, ec, a, eb, c)
+conway("(0)(1)(2)")
+

tessellations/sample/star.tes

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+## {4,6}, tromino 1S, solution 1
+s2.
+
+# we compute the edge length
+#distunit(edge(5/2,3))
+#distunit(edge(5,5/2))
+distunit(edge(5/2,5))
+
+# note: subsequent results of arcmedge are given in terms of distunit
+
+# regangle(A,B) returns the internal angle of a B-gon with sidelength A
+
+
+#let(u5 = 2*pi/3)
+#let(u5 = 4*pi/5)
+let(u5 = 2*pi/5)
+
+unittile(u5,u5,u5,u5,u5)
+
+c(0,0,0,0,0)
+c(0,1,0,3,0)
+c(0,2,0,4,0)

tessellations/sample/twothree.tes

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+## two-three tiling
+## from Marek14's post in HyperRogue discord
+e2.
+angleunit(deg)
+tile(1,90,2,90,1,90,2,90)
+tile(1,90,1,180,1,180,1,90,1,90,1,180,2,90)
+c(0,3,0,3,0)
+c(0,0,1,2,0)
+c(0,1,1,6,0)
+c(0,2,1,3,0)
+c(1,0,1,1,0)
+c(1,4,1,5,0)