Summary

Licensing

This work has been released into the public domain by its author, David Eppstein at English Wikipedia. This applies worldwide. In some countries this may not be legally possible; if so: David Eppstein grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.Public domainPublic domainfalsefalse

Source code

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

• 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].