A Hitomezashi Maker
08 Dec 2021 - Tags: pretty-pictures
It’s been a hot second since I’ve done something artistic, and a recent numberphile video gave me something small and simple to do! Plus, a really close friend of mine is a talented fibre artist, and since this type of artwork (hitomezashi) is originally a kind of decorative mending, I thought it would be fun to code this up and send it to her! It makes a great demo even without the fibre background, and I hope you all have fun playing with it ^_^.
It’s probably worth watching the video first, as otherwise it won’t make
a ton of sense what this is doing, but the idea is pretty simple:
You turn a pair of bitstrings into a pattern by reading a
It turns out the regions you build in this way are always
Apologies in advance that this is a bit slow, haha. It turns out that making graphs in sage is really not the right tool for this! Still, this gets the job done ^_^.
xxxxxxxxxxdef mkLine(n,b,d,t,sc): """ Make one row/col of the diagram. @n is the index for which row/col to make @b is the bit -- start on or start off the line @d is the direction -- is this a row or a col @t is the total number of dashes to make @sc is the color to use for the stitches """ p = Graphics() for k in range(t): if k % 2 == b: if d=="row": p += line([(n,k),(n,k+1)],rgbcolor=sc) if d=="col": p += line([(k,n),(k+1,n)],rgbcolor=sc) return pdef mkSquare(r,c,color): """ Make a square at row @r column @c with color @color """ return polygon([(r,c),(r,c+1),(r+1,c+1),(r+1,c)], rgbcolor=color, alpha=0.75)def mkPattern(rowString, colString, color1, color2, stitchColor, showBits): """ Make the whole pattern """ p = Graphics() p.set_aspect_ratio(1) p.set_axes_range(-1,len(rowString)+1,-1,len(colString)+1) # make the horizontal stitches for (n,b) in enumerate(rowString): p += mkLine(n,b,"row",len(colString),stitchColor) if showBits: p += text(b,(n, -0.5)) # make the vertical stitches for (n,b) in enumerate(colString): p += mkLine(n,b,"col",len(rowString),stitchColor) if showBits: p += text(b,(-0.5,n)) # shade in the regions cur = color1 curRow = color1 for r in range(len(rowString)): for c in range(len(colString)): if (r,c) == (0,0): p += mkSquare(r,c,cur) elif c != 0: if r%2 == colString[c]: if cur == color1: cur = color2 else: cur = color1 p += mkSquare(r,c,cur) elif c == 0: if c%2 == rowString[r]: if curRow == color1: curRow = color2 else: curRow = color1 cur = curRow p += mkSquare(r,c,cur) return pdef mkRandString(t,p): """ Make a random string of length @t of 0s and 1s 0 is chosen with probability @p """ s = [] for _ in range(t): if random() < p: s += [0] else: s += [1] return sdef stringToBits(s): """ Convert a string to a bitstring. If s is already a bitstring, leave it alone. If s is entirely numerical, reduce each digit mod 2 If s is entirely alphabetical, use vowels/consonants, like the video. Otherwise, convert to unicode and use parity. """ # we remove any spaces so that sentences can be converted as letters s = s.replace(" ", "") if s.isdigit(): return [int(c) % 2 for c in list(s)] if s.isalpha(): return [int(c in ["a", "e", "i", "o", "u"]) for c in list(s)] return [ord(c) % 2 for c in list(s)] # We have to do this hacky nested-interact thing to make everything go smoothly.# First we say whether we want the rows/cols to be randomized.# Depending on the answer, we display either a text box or a slider for each.# Then we put the aesthetic choices like colors in the innermost layer so that# changing them won't re-randomize anything from earlier layers.def _(randomRow=('randomize row?', True), randomCol=('randomize col?', True)): # we want the random starting probabilities to be interesting, # so make sure we wind up between, say, .33 and .66 r_init = round(0.33 + 0.33*random(),2) c_init = round(0.33 + 0.33*random(),2) if randomRow: if randomCol: def _(rowPercent=slider([(k/100).n(digits=2) for k in range(0,101)], default=r_init), colPercent=slider([(k/100).n(digits=2) for k in range(0,101)], default=c_init)): rowLen = randint(20,40) rowString = mkRandString(rowLen, rowPercent) colLen = randint(20,40) colString = mkRandString(colLen, colPercent) def _(color1=Color('white'), color2=Color('white'), stitchColor=Color('black'), showBits=True): print("rowString: {}".format("".join([str(b) for b in rowString]))) print("colString: {}".format("".join([str(b) for b in colString]))) show(mkPattern(rowString, colString, color1, color2, stitchColor, showBits), axes=false) else: def _(rowPercent=slider([(k/100).n(digits=2) for k in range(0,101)], default=r_init), colString=""): rowLen = randint(20,40) rowString = mkRandString(rowLen, rowPercent) colString = stringToBits(colString) def _(color1=Color('white'), color2=Color('white'), stitchColor=Color('black'), showBits=True): print("rowString: {}".format("".join([str(b) for b in rowString]))) print("colString: {}".format("".join([str(b) for b in colString]))) show(mkPattern(rowString, colString, color1, color2, stitchColor, showBits), axes=false) else: if randomCol: def _(rowString="", colPercent=slider([(k/100).n(digits=2) for k in range(0,101)], default=c_init)): rowString = stringToBits(rowString) colLen = randint(20,40) colString = mkRandString(colLen, colPercent) def _(color1=Color('white'), color2=Color('white'), stitchColor=Color('black'), showBits=True): print("rowString: {}".format("".join([str(b) for b in rowString]))) print("colString: {}".format("".join([str(b) for b in colString]))) show(mkPattern(rowString, colString, color1, color2, stitchColor, showBits), axes=false) else: def _(rowString="", colString=""): rowString = stringToBits(rowString) colString = stringToBits(colString) def _(color1=Color('white'), color2=Color('white'), stitchColor=Color('black'), showBits=True): print("rowString: {}".format("".join([str(b) for b in rowString]))) print("colString: {}".format("".join([str(b) for b in colString]))) show(mkPattern(rowString, colString, color1, color2, stitchColor, showBits), axes=false)
Later on in the video, they switch over to an isoperimetric version of this idea, where they work with triangles instead of squares, and they have three input strings. Can you write code, analogous to the above, which lets people play around with this alternative approach?