File:Regular Divisibility Lattice.svg
The Python source code for generating this image:
from math import log limit = 400 radius = 17 margin = 4 xscale = yscale = 128 skew = 0.285 def A051037(): yield 1 seq = [1] spiders = [(2,2,0,0),(3,3,0,1),(5,5,0,2)] while True: x,p,i,j = min(spiders) if x != seq[-1]: yield x seq.append(x) spiders[j] = (p*seq[i+1],p,i+1,j) def nfactors(h,p): nf = 0 while h % p == 0: nf += 1 h //= p return nf seq = [] for h in A051037(): if h > limit: break seq.append((h,nfactors(h,2),nfactors(h,3),nfactors(h,5))) leftmost = max([k for h,i,j,k in seq]) rightmost = max([j for h,i,j,k in seq]) leftwidth = int(0.5 + log(5) * leftmost * xscale + radius + margin) rightwidth = int(0.5 + log(3) * rightmost * xscale + radius + margin) width = leftwidth + rightwidth height = int(0.5 + log(limit) * yscale + 2*(radius + margin)) def place(h,i,j,k): # logical coordinates x = j * log(3) - k * log(5) + i * skew y = log(h) # physical coordinates x = (x*xscale) + leftwidth y = (-y*yscale) + height - radius - margin return (x,y) print '''<?xml version="1.0" encoding="utf-8"?> <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"> <svg xmlns="http://www.w3.org/2000/svg" version="1.1" width="%d" height="%d">''' % (width,height) print ' <g style="fill:none;stroke:#ffaaaa;">' l = 1 base = 1 while l <= limit: y = -yscale*log(l) + height - radius - margin print ' <path d="M0,%0.2fL%d,%0.2f"/>' % (y,width,y) l += base if l == 10*base: base = l print " </g>" print ' <g style="fill:none;stroke-width:1.5;stroke:#0000cc;">' def drawSegment(p,q): x1,y1=p x2,y2=q print ' <path d="M%0.2f,%0.2fL%0.2f,%0.2f"/>' % (x1,y1,x2,y2) for h,i,j,k in seq: x,y = place(h,i,j,k) if i > 0: drawSegment(place(h//2,i-1,j,k),(x,y)) if j > 0: drawSegment(place(h//3,i,j-1,k),(x,y)) if k > 0: drawSegment(place(h//5,i,j,k-1),(x,y)) print " </g>" print ' <g style="fill:#ffffff;stroke:#000000;">' for h,i,j,k in seq: x,y = place(h,i,j,k) print ' <circle cx="%0.2f" cy="%0.2f" r="%d"/>' % (x,y,radius) # pairs of first value with size: size of that value fontsizes = {1:33, 5:30, 10:27, 20:24, 100:20, 200:18} for h,i,j,k in seq: x,y = place(h,i,j,k) if h in fontsizes: print " </g>" print ' <g style="font-family:Times;font-size:%d;text-anchor:middle;">' % fontsizes[h] lower = fontsizes[h] / 3. print ' <text x="%0.2f" y="%0.2f">%d</text>' %(x,y+lower,h) print " </g>" print "</svg>"
Original upload log
The original description page was here. All following user names refer to en.wikipedia.
- 2007-03-14 05:08 David Eppstein 1363×809×0 (13167 bytes) A [[Hasse diagram]] of [[divisibility]] relationships among [[regular number]]s up to 400. Inspired by similar diagrams in a paper by Kurenniemi [http://www.beige.org/projects/dimi/CSDL2.pdf].