摘要

授權條款

此作品已由其作者，英文維基百科的David Eppstein，釋出至公有領域。此授權條款在全世界均適用。 這可能在某些國家不合法，如果是的話： David Eppstein授予任何人有權利使用此作品於任何用途，除受法律約束外，不受任何限制。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>"

原始上傳日誌

• 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].