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Original file (SVG file, nominally 1,020 × 520 pixels, file size: 615 KB)
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Summary
DescriptionOsgood curve.svg |
English: Fractal construction of an Osgood curve, a non-self-intersecting curve with nonzero area. It is formed from an initial triangle by removing a wedge connecting the apex of the triangle to the opposite side, and then doing the same thing recursively to the smaller triangles formed by this removal. At each level of the recursion, the removed wedges grow narrower, so that the amount of area removed in each level decreases exponentially, leaving a nonzero amount of area that is never removed. |
Date | |
Source | Own work |
Author | David Eppstein |
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. | |
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
Python source code
import sys
from PADS.SVG import SVG,colors
size = 500
margin = 10
triangles = [(1j,1,2+1j)]
def subdivide(triangles,fraction):
x = 0.5*(1-fraction)
for (p,q,r) in triangles:
yield (p,(1-x)*p+x*r,q)
yield (q,x*p+(1-x)*r,r)
for i in range(13):
fraction = 1./(7*1.2**i)
triangles = list(subdivide(triangles,fraction))
svg = SVG(size+(size+2*margin)*(1+1j),sys.stdout)
svg.group(style={"stroke":colors.black, "fill":colors.blue})
shift = margin*(1+1j)
for T in triangles:
points = [p*size+shift for p in T]
svg.polygon(points)
svg.ungroup()
svg.close()
# The SVG library
# from http://www.ics.uci.edu/~eppstein/PADS/SVG.py
# by David Eppstein
# http://www.ics.uci.edu/~eppstein/
"""SVG.py
Simple generation of SVG-format vector graphics files
D. Eppstein, November 2011.
"""
def _coord(x):
"""String representation for coordinate"""
return ("%.4f" % x).rstrip("0").rstrip(".")
class SVG:
def __init__(self, bbox, stream,
standalone=True, prefix=None, indentation=0):
"""Create a new SVG object, to be written to the given stream.
If standalone is True or omitted, the SVG object becomes a whole
XML file; otherwise, it becomes an XML object within a larger XML
file. If the prefix is nonempty, it is used to distinguish svg tags
from other tags; a reasonable choice for the prefix value would be
"s" or "svg". If the indentation is nonzero, it gives a number of
spaces by which every line of the file is indented.
The bbox argument should be a complex number, the farthest visible
point from the origin in the positive quadrant. The bounding box
will become the rectangle between the origin and that point.
All other methods that specify points should do so using
complex number coordinates."""
self.stream = stream
if prefix:
self.prefix = prefix + ":"
else:
self.prefix = ""
if standalone:
self.stream.write('''<?xml version="1.0"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
''')
self.indentation = indentation
self.nesting = 0
br = _coord(bbox.real)
bi = _coord(bbox.imag)
self.element('''svg width="%s" height="%s" viewBox="0 0 %s %s"
xmlns="http://www.w3.org/2000/svg" version="1.1"''' % (br,bi,br,bi),+1)
def close(self):
"""Output the end of an SVG file."""
self.element("svg", -1)
if self.nesting:
raise Exception("SVG: Unclosed tags")
def element(self, e, delta=0, unspaced=False, style={}, **morestyle):
"""Output an SVG element.
The delta argument distinguishes between XML tags that
open a nested section of the XML file (delta=+1), XML tags
that close the same section (delta=-1), and XML tags that
stand alone without anything nested inside them (delta=0).
Every call with delta=+1 must be matched by a call with delta=-1.
If the style argument is nonempty, it should be a dictionary
of style parameters, included within the object; these
may also be passed as keyword arguments to element.
If the same keyword is present both in style and as a keyword
argument, the keyword argument takes priority."""
if delta < 0:
self.nesting += delta
if delta >= 0 or not unspaced:
output = [" " * (self.indentation + 2*self.nesting), "<"]
else:
output = ["<"]
if delta < 0:
output.append("/")
output += [self.prefix, e]
style = dict(style)
style.update(morestyle)
if style:
output.append(' style="')
second = False
for keyword in style:
if second:
output.append("; ")
second = True
output += [keyword, ":", style[keyword]]
output.append('"')
if delta > 0:
self.nesting += delta
elif delta == 0:
output.append("/")
output.append(">")
if delta <= 0 or not unspaced:
output.append("\n")
self.stream.write("".join(output))
def group(self,style={},**morestyle):
"""Start a group of objects, all with the same style"""
self.element("g", +1, style=style, **morestyle)
def ungroup(self):
"""End a group of objects"""
self.element("g", -1)
def circle(self, center, radius, style={}, **morestyle):
"""Circle with given center and radius"""
self.element('circle cx="%s" cy="%s" r="%s"' %
(_coord(center.real), _coord(center.imag), _coord(radius)),
style=style, **morestyle)
def rectangle(self, p, q, style={}, **morestyle):
"""Rectangle with corners at points p and q"""
x = min(p.real,q.real)
y = min(p.imag,q.imag)
width = abs((p-q).real)
height = abs((p-q).imag)
self.element('rect x="%s" y="%s" width="%s" height="%s"' %
(_coord(x), _coord(x), _coord(width), _coord(height)),
style=style, **morestyle)
def polygon(self, points, style={}, **morestyle):
"""Polygon with corners at the given set of points"""
pointlist = " ".join(_coord(p.real)+","+_coord(p.imag) for p in points)
self.element('polygon points="%s"' % pointlist,
style=style, **morestyle)
def segment(self, p, q, style={}, **morestyle):
"""Line segment from p to q"""
self.element('line x1="%s" y1="%s" x2="%s" y2="%s"' %
(_coord(p.real), _coord(p.imag),
_coord(q.real), _coord(q.imag)), style=style, **morestyle)
def arc(self, p, q, r, large=False, style={}, **morestyle):
"""Circular arc from p to q with radius r.
If the large flag is set true, the arc will cover more than
half of a circle. The SVG "sweep-flag" is not provided;
instead, to achieve the same effect, swap p and q."""
if large:
large = "1"
else:
large = "0"
r = _coord(abs(r))
self.element('path d="M %s,%s A %s,%s 0 %s 0 %s,%s"' %
(_coord(p.real),_coord(p.imag),r,r,large,
_coord(q.real),_coord(q.imag)), style=style, **morestyle)
def text(self, label, location, style={}, **morestyle):
"""Text label at the given location.
Caller is responsible for making the label xml-safe."""
self.element('text x="%s" y="%s"' %
(_coord(location.real),_coord(location.imag)),
delta=1, unspaced=True, style=style, **morestyle)
self.stream.write(label)
self.element('text', delta=-1, unspaced=True)
# A small color palette chosen to have high contrast
# even when viewed by color-blind readers
class colors:
none = "none"
white = "#FFFFFF"
black = "#000000"
red = "#BC1E46"
blue = "#0081CD"
green = "#009246"
yellow = "#FEC200"
magenta = "#CC33CC"
Items portrayed in this file
depicts
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some value
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Creative Commons CC0 License<\/a>"}},"text\/plain":{"en":{"P275":"Creative Commons CC0 License"}}}}" class="wbmi-entityview-statementsGroup wbmi-entityview-statementsGroup-P275 oo-ui-layout oo-ui-panelLayout oo-ui-panelLayout-framed">
original creation by uploader<\/a>"}},"text\/plain":{"en":{"P7482":"original creation by uploader"}}}}" class="wbmi-entityview-statementsGroup wbmi-entityview-statementsGroup-P7482 oo-ui-layout oo-ui-panelLayout oo-ui-panelLayout-framed">
12 December 2015
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 05:22, 13 December 2015 | 1,020 × 520 (615 KB) | David Eppstein | User created page with UploadWizard |
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