%!% If you're concerned that the cpu in your PostScript printer will atrophy% from disuse, here is another Escher-like contribution to to keep it busy% for a while.  It uses PostScript color commands, but will still work on% a monochrome printer (but isn't very pretty in black & white).% % The butterflies are arranged in a hexagonal grid (wallpaper group p6),% and the moveto, lineto, curveto commands used to render the tesselation% are redefined so as to impose a nonlinear transform that shrinks the% infinite plane to an ellipse.  This is a sleazy way to mimic Escher's% "circle limit" sorts of things. %% The butterfly permimeter was made by imposing all the symmetry constraints% on a path, and then that path was filled in using Adobe Illustrator%% The routines Xform and next_color are easy to change if you want to hack% with them. The code was written to sacrifice efficiency for readability.%% Bob Wallis%% UUCP {sun,pyramid,cae780,apple}!weitek!wallis /eschersave save def		% prevent left over side effects %statusdict begin waittimeout 6000 lt	% if you have a slow printer, you%   {0 60 6000 setdefaulttimeouts}	% might need to uncomment this%if end /nlayers 1 def		% 1 takes about 10 minutes on a LW+; 2 takes 4x longer/warp 1 def		% 1 -> ellipsoidal distortion; 0 -> flat Euclidean/inch {72 mul} def  /x4 152 def /y4 205.6 def		% 6 fold rotation center of bfly/x12 387.20 def /y12 403.84 def		% 3 fold center of bfly /dx x4 x12 sub def			% [dx,dy] = distance between the/dy y4 y12 sub def			% two fixed points above /Dm dx dup mul  dy dup mul 		% magnitude of basis vectors of    add sqrt 3 sqrt mul 		% parallelogram latticedef					% = |dx,dy| * sqrt(3) /Da dy dx atan 30 add def/D1x Dm Da cos mul def			% [D1x, D1y] = basis vector vector #1/D1y Dm Da sin mul def			% = [Dm,0] exp(j30) /Da dy dx atan 30 sub def/D2x Dm Da cos mul def			% [D2x, D2y] = basis vector vector #2/D2y Dm Da sin mul def			% = [Dm,0] exp(-j30) /m { moveto} def/L {lineto} def/S {stroke} def/c {curveto} def/f {closepath fill} def/F {closepath fill} def/g { setgray} def /FillStroke {				% fill interior & stroke black border	closepath gsave fill grestore 0 setgray stroke} def %% Description of 1 butterfly%/body {	314.96 280.19 m	383.4 261.71 445.11 243.23 513.52 224.68 c	463.68 256.59 490.26 328.83 446.99 360.76 c	423.71 347.32 397.08 339.7 367.07 337.9 c	388.93 358.28 414.14 372.84 442.73 381.58 c	426.68 398.18 394.07 389.7 387.2 403.84 c	371.52 404.96 362.56 372.48 340.16 366.88 c	346.88 396.01 346.88 425.12 340.16 454.24 c	326.72 427.35 320 400.48 320 373.6 c	270.71 352.1 221.44 411.23 168.88 384.02 c	189.04 388.03 202.48 380.4 212.57 366.95 c	216.72 350.85 209.23 341.46 190.1 338.79 c	177.34 343.57 167.94 354.17 161.9 370.59 c	176.06 305.52 132.02 274.05 152 205.6 c	201.29 257.12 250.56 234.72 299.84 279.52 c	288.64 266.08 284.16 252.64 286.4 239.2 c	298.27 223.97 310.15 222.18 322.02 233.82 c	328.62 249.28 328.51 264.74 314.96 280.19 c	FillStroke} def /eyes {	294.8125 238.3246 m	296.9115 238.3246 298.6132 242.7964 298.6132 248.3125 c	298.6132 253.8286 296.9115 258.3004 294.8125 258.3004 c	292.7135 258.3004 291.0118 253.8286 291.0118 248.3125 c	291.0118 242.7964 292.7135 238.3246 294.8125 238.3246 c	closepath gsave 1 g fill grestore 0 g S		319.5 241.1782 m	321.7455 241.1782 323.5659 245.4917 323.5659 250.8125 c	323.5659 256.1333 321.7455 260.4468 319.5 260.4468 c	317.2545 260.4468 315.4341 256.1333 315.4341 250.8125 c	315.4341 245.4917 317.2545 241.1782 319.5 241.1782 c	closepath gsave 1 g fill grestore 0 g S	0 g	296.875 242.0939 m	297.4608 242.0939 297.9356 243.479 297.9356 245.1875 c	297.9356 246.896 297.4608 248.2811 296.875 248.2811 c	296.2892 248.2811 295.8143 246.896 295.8143 245.1875 c	295.8143 243.479 296.2892 242.0939 296.875 242.0939 c	f	0 g	318.5 243.7707 m	319.281 243.7707 319.9142 245.0766 319.9142 246.6875 c	319.9142 248.2984 319.281 249.6043 318.5 249.6043 c	317.719 249.6043 317.0858 248.2984 317.0858 246.6875 c	317.0858 245.0766 317.719 243.7707 318.5 243.7707 c	f} def	 /stripes {	292 289 m	252 294 241 295 213 279 c	185 263 175 252 159 222 c	S	285 313 m	239 326 226 325 206 315 c	186 305 164 278 161 267 c	S	298 353 m	262 342 251 339 237 355 c	223 371 213 380 201 383 c	S	330 288 m	384 293 385 292 418 280 c	451 268 452 264 473 247 c	S	342 306 m	381 311 386 317 410 311 c	434 305 460 287 474 262 c	S	345 321 m	352 357 359 367 379 377 c	399 387 409 385 426 382 c	S	327.75 367.75 m	336.5 392.25 333.682 403.348 335.25 415.5 c	S	320 364.75 m	322 361.75 323.5 360.5 326.25 360 c	329 359.5 332 360.5 334 362.75 c	S	316.25 356.5 m	318.75 353.25 320 353 323.25 352.25 c	326.5 351.5 329 352 331.5 353.25 c	S	312.5 349 m	316.75 345.5 318.25 344.5 321.25 343.75 c	324.25 343 327 344 329.75 346 c	S	310.75 340.75 m	314.25 336.5 316.25 335.25 320 335.25 c	323.75 335.25 327 336.5 329.25 338 c	S	308.5 332 m	311.75 328.5 312.5 327.25 317 327 c	321.5 326.75 325.75 328.25 327.75 329.75 c	S	305 322 m	309.5 317.75 310.75 317 315 316.5 c	319.25 316 322.25 318 324.75 320 c	S	302.25 311 m	307 307.5 307.75 306.25 312.75 306 c	317.75 305.75 320 307.25 323.75 309.5 c	S	301.25 298.25 m	304.5 292.75 305.25 292 308.25 292 c	311.25 292 313.75 293.75 315.75 295.75 c	S} def/nostrils {	0 g	304.062 227.775 m	304.599 227.775 305.034 228.883 305.034 230.25 c	305.034 231.616 304.599 232.724 304.062 232.724 c	303.525 232.724 303.09 231.616 303.09 230.25 c	303.09 228.883 303.525 227.775 304.062 227.775 c	f	304.062 230.25 m	F	309.562 228.275 m	310.099 228.275 310.534 229.383 310.534 230.75 c	310.534 232.116 310.099 233.224 309.562 233.224 c	309.025 233.224 308.59 232.116 308.59 230.75 c	308.59 229.383 309.025 228.275 309.562 228.275 c	f} def/thorax{	327.5 300 m	316.5 283 315.5 275.5 308 277.5 c	294 311.5 299 313.5 304 334 c	309 354.5 315.5 362 322.5 372 c	329.5 382 327.5 376.5 331 376 c	334.5 375.5 339.1367 379.1109 339 369 c	338.5 332 333.4999 324.5 330.5 311.5 c	0 g S} def/spots {	next_color	192 242.201 m	202.1535 242.201 210.3848 251.0655 210.3848 262 c	210.3848 272.9345 202.1535 281.799 192 281.799 c	181.8465 281.799 173.6152 272.9345 173.6152 262 c	173.6152 251.0655 181.8465 242.201 192 242.201 c	FillStroke	next_color	447.5 250.2365 m	459.6061 250.2365 469.4203 257.5181 469.4203 266.5 c	469.4203 275.4819 459.6061 282.7635 447.5 282.7635 c	435.3939 282.7635 425.5797 275.4819 425.5797 266.5 c	425.5797 257.5181 435.3939 250.2365 447.5 250.2365 c	FillStroke	next_color	401 369.1005 m	409.5914 369.1005 416.5563 373.5327 416.5563 379 c	416.5563 384.4673 409.5914 388.8995 401 388.8995 c	392.4086 388.8995 385.4436 384.4673 385.4436 379 c	385.4436 373.5327 392.4086 369.1005 401 369.1005 c	FillStroke	next_color	249 348.2721 m	261.4966 348.2721 271.6274 353.9707 271.6274 361 c	271.6274 368.0293 261.4966 373.7279 249 373.7279 c	236.5034 373.7279 226.3726 368.0293 226.3726 361 c	226.3726 353.9707 236.5034 348.2721 249 348.2721 c	FillStroke} def				 /ncolor 6 def/cidx 0 def /next_color {	cidx ncolor div		% hue	.75			% saturation (change these if you like)	.8			% lightness	sethsbcolor	/cidx cidx 1 add ncolor mod def} def /cidx 0 def /max_r2 	 	% radius^2 for center of outermost ring of butterflies Dm nlayers mul 1.05 mul dup mul def /max_radius max_r2 sqrt def/max_radius_inv 1 max_radius div def/Dm_inv 1 Dm div def %% Ellipsoidal distortion, maps "nlayers" concentric rings of cells into% an ellipse centered on page % D  			length of 1 basis vector separating hexagonal cells% z0			center of 6-fold rotation = origin of shrink xform% z' = (z - z0)/D 				new coord system% |z'| = sqrt(x^2 + [(8.5/11)*y]^2)		aspect ratio of paper% z" = z' * a/M(|z'|)	shrink by "a/M(|z|)" 	as fcn of radius % At the max radius, we want the shrunk ellipse to be "W" units wide so it% just fits our output format - solve for scale factor "a" % zmax = n+0.5  		for n layers of cells% zmax * [a/M(zmax)] = W	1/2 width of output on paper% a = M(zmax)*W/zmax		solve for "a" %/M{dup mul 1 add sqrt}bind def	% M(u) = sqrt(1+|u|^2) = one possible shrink/M { 1.5 add } bind def		% M(u) = (1.5+|u|)     = another possible one/W 3.8 inch def 		% 1/2 width of ellipse/zmax 0.5 nlayers add def	% radius at last layer of hexagons/a zmax M W mul zmax div def	% a = M(zmax)*W/zmax /Xform {						% [x0,y0] = ctr ellipse	Matrix transform	/y exch def	/x exch def	/z x dup mul y .773 mul dup mul add sqrt def	% ellipse radius	/Scale a z M div def				% z=a/M(|z|)	x Scale mul x0 add 				% magnify back up	y Scale mul y0 add 				% [x0+x*s, y0+y*s]} def  /Helvetica findfont 8 scalefont setfont 4.25 inch 0.5 inch moveto (RHW) stringwidth pop -0.5 mul 0 rmoveto(RHW) show				% autograph warp 1 eq {				% redefine commands to use Xform	/moveto { Xform //moveto} def	/lineto { Xform //lineto} def	/curveto { 		Xform 6 -2 roll		Xform 6 -2 roll		Xform 6 -2 roll		//curveto 	} def}if  /bfly {				% paint 1 butterfly	next_color body	1 setgray eyes	stripes	0 setgray nostrils	0.5 setgray thorax next_color	spots}  def /x0 x4 def		% center/y0 y4 def /T1matrix 			% xlate to center of image  x0 neg  y0 neg  matrix translate def /Smatrix 			% scale so that 1 basis vector = 1.0  Dm_inv dup matrix scale def /HexCell {			% 6 butterflys rotated about center of	/cidx 0 def		% 6 fold symmetry	/color 0 def	/T2matrix dx dy matrix translate def	0 60 300 {		/angle exch def		/Rmatrix angle matrix rotate def		/Matrix 	% translate, rotate, scale - used by Xform		  T1matrix Rmatrix matrix concatmatrix		  T2matrix matrix concatmatrix 		  Smatrix matrix concatmatrix 		def		gsave 		warp 0 eq 	% then may use usual PostScript machinery		{		% else using Xform			x0 y0 translate angle rotate 			.5 dup scale			dx x0 sub dy y0 sub translate		} if				bfly 		next_color		grestore	} for} def  %320 x4 sub 240 y4 sub translate 4.25 inch x4 sub 5.5 inch y4 sub translate  0 setlinewidth/N 2 defN neg 1 N {	/i exch def					% translate to	N neg 1 N {					% i*D1 + j*D2		/j exch def				% and draw HexCell		gsave		/dx i D1x mul j D2x mul add def		% translate HexCell by		/dy i D1y mul j D2y mul add def		% [dx,dy]		/r2 dx dup mul dy dup mul add def	% r^2 = |dx,dy|^2		r2 max_r2 lt				% inside radius?		{ 					% yes		1 r2 max_r2 div sub sqrt 2 div 		setlinewidth				% make skinnier lines		HexCell					% 6 butterflies		}		if		grestore	} for} for showpage clear cleardictstackeschersave restore