File:Regular divisibility lattice.svg

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Description	Regular divisibility lattice.svg A Hasse diagram of divisibility relationships among regular numbers up to 400. As shown by the horizontal light red lines, the vertical position of each number is proportional to its logarithm. Inspired by similar diagrams in a paper by Kurenniemi [1].
Date	2007-03-14 (original upload date)
Source	Originally from en.wikipedia; description page is/was here.
Author	Original uploader was David Eppstein at en.wikipedia
Permission (Reusing this image)	Released into the public domain (by the author).

[edit] Licensing

This image has been (or is hereby) released into the public domain by its author, David Eppstein at the wikipedia project. This applies worldwide. In case this is not legally possible: David Eppstein grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. العربية | Català | Česky | Dansk | Deutsch | Ελληνικά | English | Eesti | Suomi | Français | עברית | Italiano | 한국어 | Lietuvių | Македонски | Plattdüütsch | Nederlands | Polski | Română | Русский | Српски / Srpski | Svenska | ไทย | Vèneto | 中文 | ‪中文(简体)‬ | ‪中文(繁體)‬ | +/−

[edit] 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>"

[edit] Original upload log

(All 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].

File history

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The following other wikis use this file:

• Usage of Regular divisibility lattice.svg on enwiki
  • Regular number