Intrinsically Defined Curves

This plots a curve whose local curvature varies according to the choice of curvature function and multiplier. A broken-line path starting at a given position can be defined by describing a specific series of turns. More generally, you can use a function that determines the curvature at each point along a curve. Such a curve is said to be intrinsically defined. In biological systems, curvature often occurs when material is added to one side faster than another. The curvature functions in this Demonstration can be thought of as simple choices for how this difference could vary over time. They yield a variety of ordered and disordered structures.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


curvature function — the local curvature as a function of arc length
scaling factor — multiplies the curvature function
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+