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].
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
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].
Information
Captions
Add a one-line explanation of what this file represents
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].
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
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].
Information
Captions
Add a one-line explanation of what this file represents