(*^ ::[ frontEndVersion = "Microsoft Windows Mathematica Notebook Front End Version 2.2"; microsoftWindowsStandardFontEncoding; fontset = title, "Arial", 24, L0, center, nohscroll, bold; fontset = subtitle, "Arial", 18, L0, center, nohscroll, bold; fontset = subsubtitle, "Arial", 14, L0, center, nohscroll, bold; fontset = section, "Arial", 14, L0, bold, grayBox; fontset = subsection, "Arial", 12, L0, bold, blackBox; fontset = subsubsection, "Arial", 10, L0, bold, whiteBox; fontset = text, "Arial", 12, L0; fontset = smalltext, "Arial", 10, L0; fontset = input, "Courier New", 12, L0, nowordwrap, bold; fontset = output, "Courier New", 12, L0, nowordwrap; fontset = message, "Courier New", 10, L0, nowordwrap, R65280; fontset = print, "Courier New", 10, L0, nowordwrap; fontset = info, "Courier New", 10, L0, nowordwrap; fontset = postscript, "Courier New", 8, L0, nowordwrap; fontset = name, "Arial", 10, L0, nohscroll, italic, B65280; fontset = header, "Times New Roman", 10, L0, right, nohscroll; fontset = footer, "Times New Roman", 10, L0, right, nohscroll; fontset = help, "Arial", 10, L0, nohscroll; fontset = clipboard, "Arial", 12, L0, nohscroll; fontset = completions, "Arial", 12, L0, nowordwrap, nohscroll; fontset = graphics, "Courier New", 10, L0, nowordwrap, nohscroll; fontset = special1, "Arial", 12, L0, nowordwrap, nohscroll; fontset = special2, "Arial", 12, L0, center, nowordwrap, nohscroll; fontset = special3, "Arial", 12, L0, right, nowordwrap, nohscroll; fontset = special4, "Arial", 12, L0, nowordwrap, nohscroll; fontset = special5, "Arial", 12, L0, nowordwrap, nohscroll; fontset = leftheader, "Arial", 12, L0, nowordwrap, nohscroll; fontset = leftfooter, "Arial", 12, L0, nowordwrap, nohscroll; fontset = reserved1, "Courier New", 10, L0, nowordwrap, nohscroll;] :[font = subsubtitle; inactive; nohscroll; center; ] Self-Similar Fractals :[font = smalltext; inactive; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; plain; fontName = "Arial"; fontSize = 10; ] Bruce Ikenaga - 5-26-95 :[font = text; inactive; ] This is a package for generating self-similar fractals. A generator consists of a sequence of segments; an initiator consists of a sequence of segments. At each step, a scaled copy of the generator replaces each segment in the current sequence, beginning with the initiator. The functions return lists of points, which may be displayed or manipulated in other ways. :[font = subsection; inactive; startGroup; Cclosed; ] Sample initiators. :[font = input; initialization; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) triangle = N[{{0, 0}, {1, 0}, {1/2, 3^(1/2)/2}, {0, 0}}, 20]; (* :[font = input; initialization; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) square = N[{{0, 0}, {1, 0}, {1, 1}, {0, 1}, {0, 0}}]; (* :[font = input; initialization; endGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) segment = N[{{0, 0}, {1, 0}}]; (* :[font = subsection; inactive; startGroup; Cclosed; ] Sample Generators :[font = subsubsection; inactive; initialization; startGroup; ] *) A square "hump" (* :[font = input; initialization; endGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) sqhump = N[{{1/3, 0}, {1/3, 1/3}, {2/3, 1/3}, {2/3, 0}}]; (* :[font = subsubsection; inactive; initialization; startGroup; ] *) A triangular "hump" (* :[font = input; initialization; endGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) trihump = N[{{1/3, 0}, {1/2, 3^(1/2)/6}, {2/3, 0}}, 20]; (* :[font = subsubsection; inactive; initialization; startGroup; ] *) A right-triangular "sawtooth" at the right end of a segment (* :[font = input; initialization; endGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) rightsaw = N[{{1/2, 0}, {1, 1/2}}]; (* :[font = subsubsection; inactive; initialization; startGroup; ] *) An "on" square pulse followed by an "off" square pulse; the two pulses occupy the middle half of the interval. The first version has height 1/4; the second has height 1/2. The third has height 1/2, and the midpoint of the interval is one of the points in the generator. (* :[font = input; initialization; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) smsqwave = N[{{1/4, 0}, {1/4, 1/4}, {1/2, 1/4}, {1/2, 0}, {1/2, -1/4}, {3/4, -1/4}, {3/4, 0}}]; (* :[font = input; initialization; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) lgsqwave = N[{{0, 1/2}, {1/2, 1/2}, {1/2, -1/2}, {1, -1/2}}]; (* :[font = input; initialization; endGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) lqsqwavemid = N[{{0, 1/2}, {1/2, 1/2}, {1/2, 0}, {1/2, -1/2}, {1, -1/2}}]; (* :[font = subsubsection; inactive; startGroup; ] An S-shape :[font = input; endGroup; endGroup; nowordwrap; ] sshape = N[{{1/4,0},{1/4,1/4},{1/2,1/4},{1/2,0}, {1/2,-1/4},{3/4,-1/4},{3/4,0}}]; :[font = subsection; inactive; startGroup; Cclosed; ] Implementation :[font = input; initialization; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) Grab::usage = "Grab[mylist, n] returns a list containing the n-th and (n + 1)-st elements of mylist."; (* :[font = input; initialization; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) SpliceList::usage = "SpliceList[mylist, chunk, n] inserts the elements in the list chunk in the list mylist after position n, and returns the spliced list."; (* :[font = input; initialization; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) Rotate::usage = "Rotate[theta] returns a 2 x 2 matrix which implements a counterlockwise rotation through theta."; (* :[font = input; initialization; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) Distance::usage = "Distance[{x1, y1}, {x2, y2}] returns the distance from {x1, y1} to {x2, y2}."; (* :[font = input; initialization; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) StdAngle::usage = "StdAngle[{x1, y1}, {x2, y2}] returns the angle in the range (-Pi, Pi] that the vector from {x1, y1} to {x2, y2} makes with a ray parallel to the positive x-axis."; (* :[font = input; initialization; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) Restore::usage = "Restore[mylist, myangle, {dx, dy}, scale] takes the list mylist of vectors, multiplies them by scale, rotates them through myangle, and translates them by {dx, dy}, returning the transformed list."; (* :[font = input; initialization; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) Generate::usage = "Generate[mylist, myrule] returns the list obtained by applying the fractal generator myrule to mylist."; (* :[font = input; initialization; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) SelfSimilarFractal::usage = "SelfSimilarFractal[mylist, myrule, n] starts with the initiator determined by the points in mylist, and applies the rule given by myrule n times. It returns the list of points in the n-th generation."; (* :[font = input; initialization; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) MakeFractal::usage = "MakeFractal[filename, fractalname, initiator, generator, n, ] generates the n-th generation of the fractal starting from initiator (a list of points) using generator (a list of points based on the segment from {0, 0} to {1, 0}, with the endpoints implied). The list of points comprising the fractal is written to the expression fractalname in the file filename; the time for *each* generation is printed on the console, and optionally logged in logfile (which defaults to stdout)."; (* :[font = input; initialization; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) Grab[mylist_List, n_Integer?Positive] := Take[mylist, {n, n + 1}]; (* :[font = input; initialization; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) SpliceList[mylist_, chunk_, n_Integer?Positive] := Module[ {pos, chunksize = Length[chunk], newlist = mylist}, For[pos = 1, pos <= chunksize, pos++, newlist = Insert[newlist, chunk[[pos]], n + pos] ]; Return[newlist] ]; (* :[font = input; initialization; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) Rotate[ang_] := N[{{Cos[ang], -Sin[ang]}, {Sin[ang], Cos[ang]}}]; (* :[font = input; initialization; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) Distance[{x1_, y1_}, {x2_, y2_}] := N[((x2 - x1)^2 + (y2 - y1)^2 )^(1/2)]; (* :[font = input; initialization; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) StdAngle[{x1_, y1_}, {x2_, y2_}] := Module[{dx = x2 - x1, dy = y2 - y1}, If[dx == 0, If[dy == 0, Return[0], Return[N[(Pi/2) Sign[dy]]] ], If[dy == 0, Return[N[(Pi/2) (1 - Sign[dx])]], If[dx > 0, Return[N[ArcTan[dy/dx]]], Return[N[Pi Sign[dy] + ArcTan[dy/dx]]] ] ] ] ]; (* :[font = input; initialization; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) Restore[mylist_, angle_, {dx_, dy_}, scale_] := Module[{i, size = Length[mylist], newlist = {}}, For[i = 1, i <= size, i++, newlist = AppendTo[newlist, N[{dx, dy} + scale (Rotate[angle] . mylist[[i]])]] ]; Return[newlist] ]; (* :[font = input; initialization; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) Generate[mylist_, myrule_] := Module[{i, size = Length[mylist], newlist = mylist, pair, angle, norm}, For[i = size - 1, i > 0, i--, (pair = Grab[newlist, i]; angle = StdAngle[pair[[1]], pair[[2]]]; norm = Distance[pair[[1]], pair[[2]]]; newlist = SpliceList[newlist, Restore[myrule, angle, pair[[1]], norm], i] ) ]; Return[newlist] ]; (* :[font = input; initialization; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) SelfSimilarFractal[mylist_, myrule_, n_] := Module[{i, newlist = mylist}, For[i = 1, i <= n, i ++, newlist = Generate[newlist, myrule]]; Return[newlist] ]; (* :[font = input; initialization; endGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] *) MakeFractal[filename_, fractalname_, initiator_, generator_, n_, logfile_:stdout] := (OpenAppend[logfile]; Module[{mycount, mytime}, For[mycount = 1, mycount <= n, mycount++, If[mycount == 1, mytime = Timing[Generate[initiator, generator]]; fractalname = mytime[[2]]; Save[filename, fractalname]; Print["Generation ", mycount, " took ", mytime[[1]]]; Write[logfile, "Generation ", mycount, " took ", mytime[[1]]], (* else mycount > 1 *) OpenRead[filename]; Get[filename]; Close[filename]; mytime = Timing[Generate[fractalname, generator]]; fractalname = mytime[[2]]; OpenWrite[filename]; Close[filename]; Save[filename, fractalname]; Print["Generation ", mycount, " took ", mytime[[1]]]; Write[logfile, "Generation ", mycount, " took ", mytime[[1]]] ] ]; ]; Close[logfile]; Remove[fractalname] ); (* :[font = subsection; inactive; startGroup; Cclosed; ] Sample :[font = input; nowordwrap; ] smsqhump = {{0.25, 0}, {0.25, 0.25}, {0.5, 0.25}, {0.5, 0}, {0.75, 0}}; :[font = input; nowordwrap; ] mylist = SelfSimilarFractal[square, sqhump, 4]; :[font = input; startGroup; nowordwrap; ] Show[Graphics[Line[mylist]], AspectRatio->Automatic] :[font = postscript; inactive; output; endGroup; endGroup; BITMAP; PostScript; pictureLeft = 100; pictureTop = 0; pictureWidth = 300; pictureHeight = 300; 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Mistroke .51488 .37667 L .51488 .37295 L .5186 .37295 L .5186 .36923 L .51488 .36923 L .51116 .36923 L .51116 .36551 L .51488 .36551 L .51488 .36179 L .51116 .36179 L .51116 .35807 L .50744 .35807 L .50744 .36179 L .50744 .36551 L .50372 .36551 L .50372 .36179 L .5 .36179 L .49628 .36179 L .49628 .35807 L .49256 .35807 L .49256 .36179 L .49256 .36551 L .48884 .36551 L .48884 .36179 L .48512 .36179 L .48512 .35807 L .48884 .35807 L .48884 .35435 L .48512 .35435 L .4814 .35435 L .4814 .35063 L .48512 .35063 L .48512 .34691 L .48884 .34691 L .48884 .35063 L .49256 .35063 L .49256 .34691 L .49256 .34319 L .49628 .34319 L .49628 .34691 L .5 .34691 L .5 .34319 L .50372 .34319 L .50372 .33947 L .5 .33947 L .49628 .33947 L .49628 .33575 L .5 .33575 L .5 .33203 L .5 .32831 L Mistroke .50372 .32831 L .50372 .32459 L .5 .32459 L .49628 .32459 L .49628 .32087 L .5 .32087 L .5 .31715 L .50372 .31715 L .50372 .32087 L .50744 .32087 L .50744 .31715 L .50744 .31343 L .51116 .31343 L .51116 .31715 L .51488 .31715 L .51488 .31343 L .5186 .31343 L .5186 .30971 L .51488 .30971 L .51116 .30971 L .51116 .30599 L .51488 .30599 L .51488 .30227 L .51116 .30227 L .51116 .29855 L .50744 .29855 L .50744 .30227 L .50744 .30599 L .50372 .30599 L .50372 .30227 L .5 .30227 L .49628 .30227 L .49628 .29855 L .49256 .29855 L .49256 .30227 L .49256 .30599 L .48884 .30599 L .48884 .30227 L .48512 .30227 L .48512 .29855 L .48884 .29855 L .48884 .29483 L .48512 .29483 L .4814 .29483 L .4814 .29111 L .48512 .29111 L .48512 .28739 L .48884 .28739 L .48884 .29111 L .49256 .29111 L Mistroke .49256 .28739 L .49256 .28367 L .49628 .28367 L .49628 .28739 L .5 .28739 L .5 .28367 L .50372 .28367 L .50372 .27995 L .5 .27995 L .49628 .27995 L .49628 .27623 L .5 .27623 L .5 .27251 L .50372 .27251 L .50372 .27623 L .50744 .27623 L .50744 .27251 L .50744 .26879 L .51116 .26879 L .51116 .27251 L .51488 .27251 L .51488 .27623 L .51116 .27623 L .51116 .27995 L .51488 .27995 L .5186 .27995 L .5186 .28367 L .51488 .28367 L .51488 .28739 L .5186 .28739 L .5186 .29111 L .52232 .29111 L .52232 .28739 L .52232 .28367 L .52604 .28367 L .52604 .28739 L .52976 .28739 L .52976 .28367 L .53348 .28367 L .53348 .27995 L .52976 .27995 L .52604 .27995 L .52604 .27623 L .52976 .27623 L .52976 .27251 L .52976 .26879 L .53348 .26879 L .53348 .26507 L .52976 .26507 L .52604 .26507 L Mistroke .52604 .26135 L .52976 .26135 L .52976 .25763 L .53348 .25763 L .53348 .26135 L .5372 .26135 L .5372 .25763 L .5372 .25391 L .54092 .25391 L .54092 .25763 L .54464 .25763 L .54464 .26135 L .54092 .26135 L .54092 .26507 L .54464 .26507 L .54836 .26507 L .54836 .26879 L .54464 .26879 L .54464 .27251 L .54836 .27251 L .54836 .27623 L .55208 .27623 L .55208 .27251 L .55208 .26879 L .5558 .26879 L .5558 .27251 L .55952 .27251 L .55952 .26879 L .56324 .26879 L .56324 .26507 L .55952 .26507 L .5558 .26507 L .5558 .26135 L .55952 .26135 L .55952 .25763 L .56324 .25763 L .56324 .26135 L .56696 .26135 L .56696 .25763 L .56696 .25391 L .57068 .25391 L .57068 .25763 L .5744 .25763 L .5744 .25391 L .57813 .25391 L .57813 .25019 L .5744 .25019 L .57068 .25019 L .57068 .24647 L .5744 .24647 L Mistroke .5744 .24275 L .57068 .24275 L .57068 .23903 L .56696 .23903 L .56696 .24275 L .56696 .24647 L .56324 .24647 L .56324 .24275 L .55952 .24275 L .5558 .24275 L .5558 .23903 L .55208 .23903 L .55208 .24275 L .55208 .24647 L .54836 .24647 L .54836 .24275 L .54464 .24275 L .54464 .23903 L .54836 .23903 L .54836 .23531 L .54464 .23531 L .54092 .23531 L .54092 .23158 L .54464 .23158 L .54464 .22786 L .54836 .22786 L .54836 .23158 L .55208 .23158 L .55208 .22786 L .55208 .22414 L .5558 .22414 L .5558 .22786 L .55952 .22786 L .55952 .22414 L .56324 .22414 L .56324 .22042 L .55952 .22042 L .5558 .22042 L .5558 .2167 L .55952 .2167 L .55952 .21298 L .5558 .21298 L .5558 .20926 L .55208 .20926 L .55208 .21298 L .55208 .2167 L .54836 .2167 L .54836 .21298 L .54464 .21298 L .54464 .20926 L Mistroke .54836 .20926 L .54836 .20554 L .54464 .20554 L .54092 .20554 L .54092 .20182 L .54464 .20182 L .54464 .1981 L .54092 .1981 L .54092 .19438 L .5372 .19438 L .5372 .1981 L .5372 .20182 L .53348 .20182 L .53348 .1981 L .52976 .1981 L .52976 .20182 L .52604 .20182 L .52604 .20554 L .52976 .20554 L .53348 .20554 L .53348 .20926 L .52976 .20926 L .52976 .21298 L .52976 .2167 L .52604 .2167 L .52604 .22042 L .52976 .22042 L .53348 .22042 L .53348 .22414 L .52976 .22414 L .52976 .22786 L .52604 .22786 L .52604 .22414 L .52232 .22414 L .52232 .22786 L .52232 .23158 L .5186 .23158 L .5186 .22786 L .51488 .22786 L .51488 .22414 L .5186 .22414 L .5186 .22042 L .51488 .22042 L .51116 .22042 L .51116 .2167 L .51488 .2167 L .51488 .21298 L .51116 .21298 L .51116 .20926 L .50744 .20926 L Mistroke .50744 .21298 L .50744 .2167 L .50372 .2167 L .50372 .21298 L .5 .21298 L .49628 .21298 L .49628 .20926 L .49256 .20926 L .49256 .21298 L .49256 .2167 L .48884 .2167 L .48884 .21298 L .48512 .21298 L .48512 .20926 L .48884 .20926 L .48884 .20554 L .48512 .20554 L .4814 .20554 L .4814 .20182 L .48512 .20182 L .48512 .1981 L .4814 .1981 L .4814 .19438 L .47768 .19438 L .47768 .1981 L .47768 .20182 L .47396 .20182 L .47396 .1981 L .47024 .1981 L .47024 .20182 L .46652 .20182 L .46652 .20554 L .47024 .20554 L .47396 .20554 L .47396 .20926 L .47024 .20926 L .47024 .21298 L .47024 .2167 L .46652 .2167 L .46652 .22042 L .47024 .22042 L .47396 .22042 L .47396 .22414 L .47024 .22414 L .47024 .22786 L .46652 .22786 L .46652 .22414 L .4628 .22414 L .4628 .22786 L .4628 .23158 L Mistroke .45908 .23158 L .45908 .22786 L .45536 .22786 L .45536 .22414 L .45908 .22414 L .45908 .22042 L .45536 .22042 L .45164 .22042 L .45164 .2167 L .45536 .2167 L .45536 .21298 L .45164 .21298 L .45164 .20926 L .44792 .20926 L .44792 .21298 L .44792 .2167 L .4442 .2167 L .4442 .21298 L .44048 .21298 L .44048 .20926 L .4442 .20926 L .4442 .20554 L .44048 .20554 L .43676 .20554 L .43676 .20182 L .44048 .20182 L .44048 .1981 L .4442 .1981 L .4442 .20182 L .44792 .20182 L .44792 .1981 L .44792 .19438 L .45164 .19438 L .45164 .1981 L .45536 .1981 L .45536 .19438 L .45908 .19438 L .45908 .19066 L .45536 .19066 L .45164 .19066 L .45164 .18694 L .45536 .18694 L .45536 .18322 L .45164 .18322 L .45164 .1795 L .44792 .1795 L .44792 .18322 L .44792 .18694 L .4442 .18694 L .4442 .18322 L Mistroke .44048 .18322 L .43676 .18322 L .43676 .1795 L .43304 .1795 L .43304 .18322 L .43304 .18694 L .42932 .18694 L .42932 .18322 L .4256 .18322 L .4256 .1795 L .42932 .1795 L .42932 .17578 L .4256 .17578 L .42188 .17578 L .42188 .17206 L .4256 .17206 L .4256 .16834 L .42932 .16834 L .42932 .17206 L .43304 .17206 L .43304 .16834 L .43304 .16462 L .43676 .16462 L .43676 .16834 L .44048 .16834 L .44048 .16462 L .4442 .16462 L .4442 .1609 L .44048 .1609 L .43676 .1609 L .43676 .15718 L .44048 .15718 L .44048 .15346 L .4442 .15346 L .4442 .15718 L .44792 .15718 L .44792 .15346 L .44792 .14974 L .45164 .14974 L .45164 .15346 L .45536 .15346 L .45536 .15718 L .45164 .15718 L .45164 .1609 L .45536 .1609 L .45908 .1609 L .45908 .16462 L .45536 .16462 L .45536 .16834 L .45908 .16834 L Mistroke .45908 .17206 L .4628 .17206 L .4628 .16834 L .4628 .16462 L .46652 .16462 L .46652 .16834 L .47024 .16834 L .47024 .16462 L .47396 .16462 L .47396 .1609 L .47024 .1609 L .46652 .1609 L .46652 .15718 L .47024 .15718 L .47024 .15346 L .47024 .14974 L .47396 .14974 L .47396 .14602 L .47024 .14602 L .46652 .14602 L .46652 .1423 L .47024 .1423 L .47024 .13858 L .47396 .13858 L .47396 .1423 L .47768 .1423 L .47768 .13858 L .47768 .13486 L .4814 .13486 L .4814 .13858 L .48512 .13858 L .48512 .1423 L .4814 .1423 L .4814 .14602 L .48512 .14602 L .48884 .14602 L .48884 .14974 L .48512 .14974 L .48512 .15346 L .48884 .15346 L .48884 .15718 L .49256 .15718 L .49256 .15346 L .49256 .14974 L .49628 .14974 L .49628 .15346 L .5 .15346 L .5 .14974 L .50372 .14974 L .50372 .14602 L Mistroke .5 .14602 L .49628 .14602 L .49628 .1423 L .5 .1423 L .5 .13858 L .50372 .13858 L .50372 .1423 L .50744 .1423 L .50744 .13858 L .50744 .13486 L .51116 .13486 L .51116 .13858 L .51488 .13858 L .51488 .13486 L .5186 .13486 L .5186 .13114 L .51488 .13114 L .51116 .13114 L .51116 .12742 L .51488 .12742 L .51488 .1237 L .51116 .1237 L .51116 .11998 L .50744 .11998 L .50744 .1237 L .50744 .12742 L .50372 .12742 L .50372 .1237 L .5 .1237 L .49628 .1237 L .49628 .11998 L .49256 .11998 L .49256 .1237 L .49256 .12742 L .48884 .12742 L .48884 .1237 L .48512 .1237 L .48512 .11998 L .48884 .11998 L .48884 .11626 L .48512 .11626 L .4814 .11626 L .4814 .11254 L .48512 .11254 L .48512 .10882 L .48884 .10882 L .48884 .11254 L .49256 .11254 L .49256 .10882 L .49256 .1051 L Mistroke .49628 .1051 L .49628 .10882 L .5 .10882 L .5 .1051 L .50372 .1051 L .50372 .10138 L .5 .10138 L .49628 .10138 L .49628 .09766 L .5 .09766 L .5 .09394 L .50372 .09394 L .50372 .09766 L .50744 .09766 L .50744 .09394 L .50744 .09022 L .51116 .09022 L .51116 .09394 L .51488 .09394 L .51488 .09766 L .51116 .09766 L .51116 .10138 L .51488 .10138 L .5186 .10138 L .5186 .1051 L .51488 .1051 L .51488 .10882 L .5186 .10882 L .5186 .11254 L .52232 .11254 L .52232 .10882 L .52232 .1051 L .52604 .1051 L .52604 .10882 L .52976 .10882 L .52976 .1051 L .53348 .1051 L .53348 .10138 L .52976 .10138 L .52604 .10138 L .52604 .09766 L .52976 .09766 L .52976 .09394 L .52976 .09022 L .53348 .09022 L .53348 .0865 L .52976 .0865 L .52604 .0865 L .52604 .08278 L .52976 .08278 L Mistroke .52976 .07906 L .53348 .07906 L .53348 .08278 L .5372 .08278 L .5372 .07906 L .5372 .07533 L .54092 .07533 L .54092 .07906 L .54464 .07906 L .54464 .08278 L .54092 .08278 L .54092 .0865 L .54464 .0865 L .54836 .0865 L .54836 .09022 L .54464 .09022 L .54464 .09394 L .54836 .09394 L .54836 .09766 L .55208 .09766 L .55208 .09394 L .55208 .09022 L .5558 .09022 L .5558 .09394 L .55952 .09394 L .55952 .09766 L .5558 .09766 L .5558 .10138 L .55952 .10138 L .56324 .10138 L .56324 .1051 L .55952 .1051 L .55952 .10882 L .5558 .10882 L .5558 .1051 L .55208 .1051 L .55208 .10882 L .55208 .11254 L .54836 .11254 L .54836 .10882 L .54464 .10882 L .54464 .11254 L .54092 .11254 L .54092 .11626 L .54464 .11626 L .54836 .11626 L .54836 .11998 L .54464 .11998 L .54464 .1237 L .54836 .1237 L Mistroke .54836 .12742 L .55208 .12742 L .55208 .1237 L .55208 .11998 L .5558 .11998 L .5558 .1237 L .55952 .1237 L .56324 .1237 L .56324 .12742 L .56696 .12742 L .56696 .1237 L .56696 .11998 L .57068 .11998 L .57068 .1237 L .5744 .1237 L .5744 .12742 L .57068 .12742 L .57068 .13114 L .5744 .13114 L .57813 .13114 L .57813 .13486 L .5744 .13486 L .5744 .13858 L .57068 .13858 L .57068 .13486 L .56696 .13486 L .56696 .13858 L .56696 .1423 L .56324 .1423 L .56324 .13858 L .55952 .13858 L .55952 .1423 L .5558 .1423 L .5558 .14602 L .55952 .14602 L .56324 .14602 L .56324 .14974 L .55952 .14974 L .55952 .15346 L .56324 .15346 L .56324 .15718 L .56696 .15718 L .56696 .15346 L .56696 .14974 L .57068 .14974 L .57068 .15346 L .5744 .15346 L .5744 .15718 L .57068 .15718 L .57068 .1609 L Mistroke .5744 .1609 L .57813 .1609 L .57813 .16462 L .5744 .16462 L .5744 .16834 L .57813 .16834 L .57813 .17206 L .58185 .17206 L .58185 .16834 L .58185 .16462 L .58557 .16462 L .58557 .16834 L .58929 .16834 L .58929 .16462 L .59301 .16462 L .59301 .1609 L .58929 .1609 L .58557 .1609 L .58557 .15718 L .58929 .15718 L .58929 .15346 L .58929 .14974 L .59301 .14974 L .59301 .14602 L .58929 .14602 L .58557 .14602 L .58557 .1423 L .58929 .1423 L .58929 .13858 L .59301 .13858 L .59301 .1423 L .59673 .1423 L .59673 .13858 L .59673 .13486 L .60045 .13486 L .60045 .13858 L .60417 .13858 L .60417 .1423 L .60045 .1423 L .60045 .14602 L .60417 .14602 L .60789 .14602 L .60789 .14974 L .60417 .14974 L .60417 .15346 L .60789 .15346 L .60789 .15718 L .61161 .15718 L .61161 .15346 L .61161 .14974 L Mistroke .61533 .14974 L .61533 .15346 L .61905 .15346 L .61905 .14974 L .62277 .14974 L .62277 .14602 L .61905 .14602 L .61533 .14602 L .61533 .1423 L .61905 .1423 L .61905 .13858 L .62277 .13858 L .62277 .1423 L .62649 .1423 L .62649 .13858 L .62649 .13486 L .63021 .13486 L .63021 .13858 L .63393 .13858 L .63393 .13486 L .63765 .13486 L .63765 .13114 L .63393 .13114 L .63021 .13114 L .63021 .12742 L .63393 .12742 L .63393 .1237 L .63021 .1237 L .63021 .11998 L .62649 .11998 L .62649 .1237 L .62649 .12742 L .62277 .12742 L .62277 .1237 L .61905 .1237 L .61533 .1237 L .61533 .11998 L .61161 .11998 L .61161 .1237 L .61161 .12742 L .60789 .12742 L .60789 .1237 L .60417 .1237 L .60417 .11998 L .60789 .11998 L .60789 .11626 L .60417 .11626 L .60045 .11626 L .60045 .11254 L .60417 .11254 L Mistroke .60417 .10882 L .60789 .10882 L .60789 .11254 L .61161 .11254 L .61161 .10882 L .61161 .1051 L .61533 .1051 L .61533 .10882 L .61905 .10882 L .61905 .1051 L .62277 .1051 L .62277 .10138 L .61905 .10138 L .61533 .10138 L .61533 .09766 L .61905 .09766 L .61905 .09394 L .61905 .09022 L .62277 .09022 L .62277 .0865 L .61905 .0865 L .61533 .0865 L .61533 .08278 L .61905 .08278 L 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.68229 .15718 L .68229 .15346 L Mistroke .67857 .15346 L .67857 .15718 L .67485 .15718 L .67485 .1609 L .67857 .1609 L .68229 .1609 L .68229 .16462 L .67857 .16462 L .67857 .16834 L .67485 .16834 L .67485 .16462 L .67113 .16462 L .67113 .16834 L .67113 .17206 L .66741 .17206 L .66741 .16834 L .66369 .16834 L .66369 .17206 L .65997 .17206 L .65997 .17578 L .66369 .17578 L .66741 .17578 L .66741 .1795 L .66369 .1795 L .66369 .18322 L .66741 .18322 L .66741 .18694 L .67113 .18694 L .67113 .18322 L .67113 .1795 L .67485 .1795 L .67485 .18322 L .67857 .18322 L .68229 .18322 L .68229 .18694 L .68601 .18694 L .68601 .18322 L .68601 .1795 L .68973 .1795 L .68973 .18322 L .69345 .18322 L .69345 .18694 L .68973 .18694 L .68973 .19066 L .69345 .19066 L .69717 .19066 L .69717 .19438 L .69345 .19438 L .69345 .1981 L .68973 .1981 L Mistroke .68973 .19438 L .68601 .19438 L .68601 .1981 L .68601 .20182 L .68229 .20182 L .68229 .1981 L .67857 .1981 L .67857 .20182 L .67485 .20182 L .67485 .20554 L .67857 .20554 L .68229 .20554 L .68229 .20926 L .67857 .20926 L .67857 .21298 L .68229 .21298 L .68229 .2167 L .68601 .2167 L .68601 .21298 L .68601 .20926 L .68973 .20926 L .68973 .21298 L .69345 .21298 L .69345 .2167 L .68973 .2167 L .68973 .22042 L .69345 .22042 L .69717 .22042 L .69717 .22414 L .69345 .22414 L .69345 .22786 L .69717 .22786 L .69717 .23158 L .70089 .23158 L .70089 .22786 L .70089 .22414 L .70461 .22414 L .70461 .22786 L .70833 .22786 L .70833 .22414 L .71205 .22414 L .71205 .22042 L .70833 .22042 L .70461 .22042 L .70461 .2167 L .70833 .2167 L .70833 .21298 L .70833 .20926 L .71205 .20926 L .71205 .20554 L Mistroke .70833 .20554 L .70461 .20554 L .70461 .20182 L .70833 .20182 L .70833 .1981 L .71205 .1981 L .71205 .20182 L .71577 .20182 L .71577 .1981 L .71577 .19438 L .71949 .19438 L .71949 .1981 L .72321 .1981 L .72321 .20182 L .71949 .20182 L .71949 .20554 L .72321 .20554 L .72693 .20554 L .72693 .20926 L .72321 .20926 L .72321 .21298 L .72693 .21298 L .72693 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.31715 L .95015 .31715 L .95015 .32087 L .95387 .32087 L .95387 .31715 L .95387 .31343 L .95759 .31343 L .95759 .31715 L .96131 .31715 L .96131 .32087 L .95759 .32087 L .95759 .32459 L .96131 .32459 L .96503 .32459 L .96503 .32831 L .96131 .32831 L .96131 .33203 L .96503 .33203 L .96503 .33575 L .96875 .33575 L .96875 .33203 L .96875 .32831 L .97247 .32831 L .97247 .33203 L .97619 .33203 L Mfstroke % End of Graphics MathPictureEnd :[font = subsection; inactive; startGroup; Cclosed; ] Yet another sample :[font = input; nowordwrap; ] mylist = SelfSimilarFractal[segment, trihump, 2]; :[font = input; startGroup; nowordwrap; ] Show[Graphics[Line[mylist]], AspectRatio->Automatic] :[font = postscript; inactive; output; endGroup; BITMAP; PostScript; pictureLeft = 100; pictureTop = 0; pictureWidth = 300; pictureHeight = 87; nowordwrap; ] %! %%Creator: Mathematica %%AspectRatio: .28868 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.00687322 0.952381 [ [ 0 0 0 0 ] [ 1 .28868 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P 0 0 m 1 0 L 1 .28868 L 0 .28868 L closepath clip newpath .004 w .02381 .00687 m .12963 .00687 L .18254 .09852 L .23545 .00687 L .34127 .00687 L .39418 .09852 L .34127 .19016 L .44709 .19016 L .5 .2818 L .55291 .19016 L .65873 .19016 L .60582 .09852 L .65873 .00687 L .76455 .00687 L .81746 .09852 L .87037 .00687 L .97619 .00687 L s % End of Graphics MathPictureEnd :[font = input; nowordwrap; ] mylist = SelfSimilarFractal[segment, trihump, 4]; :[font = input; startGroup; nowordwrap; ] Show[Graphics[Line[mylist]], AspectRatio->Automatic] :[font = postscript; inactive; output; endGroup; endGroup; BITMAP; PostScript; pictureLeft = 100; pictureTop = 0; pictureWidth = 300; pictureHeight = 87; nowordwrap; ] %! %%Creator: Mathematica %%AspectRatio: .28868 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 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.03742 L .85861 .02724 L .87037 .02724 L .86449 .01706 L .87037 .00687 L .88213 .00687 L .88801 .01706 L .89389 .00687 L .90564 .00687 L .91152 .01706 L .90564 .02724 L .9174 .02724 L .92328 .03742 L .92916 .02724 L Mistroke .94092 .02724 L .93504 .01706 L .94092 .00687 L .95267 .00687 L .95855 .01706 L .96443 .00687 L .97619 .00687 L Mfstroke % End of Graphics MathPictureEnd :[font = subsection; inactive; startGroup; Cclosed; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Arial"; fontSize = 12; ] A square wave on a square :[font = input; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] mylist = SelfSimilarFractal[square, smsqwave, 5]; :[font = input; endGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] Show[Graphics[Line[mylist]], AspectRatio->Automatic] ^*)