Curvature of the Mind

Thoughts from a Recreational Physicist

Now with Movement

September 7, 2010 by Andy Brummer 5 Comments

simple fractal

One of the nice things about these images is that they give me the opportunity to talk about some of the more abstract mathematical concepts in a natural environment. These images are rough and don’t look anything like the functions from algebra and calculus, but the are built out of those same simple functions.

The first thing I’d like to talk about is continuity. These images lack many features that I would consider important for a shape. They don’t have distinct edges, sides or middles. Some are just groups of distinct blobs and others are nebulous clouds which don’t look much like anything at all.

In spite of that each one has a well defined “size” and it is possible to overlay two shapes, subtract one from the other and compute the “size” of the difference. This gives a basic concept of distance between the shapes.

One of the neat things about this distance is that you can show the shape generated by these equations depends continuously on the parameters of the equations, so changing one of the numbers slightly produces a correspondingly small change in the shape. That’s what inspired my next page, a random path through a small image space over time.

The images slowly blend and blur into each other over time without jumps or tears, precisely because of that continuity.

animate

Filed Under: Experiments Tagged With: chrome, fractal, ifs, iterated function system

Logging In...

Profile cancel

Sign in with Twitter Sign in with Facebook
or

Not published

  • 5 Replies
  • 5 Comments
  • 0 Tweets
  • 0 Facebook
  • 0 Pingbacks
Last reply was October 5, 2010
  1. Carrie Davis
    View September 8, 2010

    I have absolutely no idea what this is all about, but the animation is beautiful!

  2. Andy
    View September 9, 2010

    Thanks Carrie, I’m having a blast playing with this stuff and there is even better looking stuff on the way.

  3. Krysten Knouse
    View September 30, 2010

    Have any person tried using this kind of previously?

    [WORDPRESS HASHCASH] The poster sent us ‘0 which is not a hashcash value.

  4. Andy
    View October 5, 2010

    It’s only been tested with chrome, firefox, IE9 or safari.

  5. Andy
    View October 5, 2010

    These fractals have been around since the 80’s. I haven’t seen them with javascript and canvas in the browser though.

pages

  • 3D harmonic oscillator eigenfunctions
  • About
  • Images
    • 2 simple
    • atomic
    • IFS fractals: 2 transformations
    • random
  • Inspiration
  • Work
    • Atomic Orbitals
    • The surprises keep comming
    • Voronoi

Copyright © 2021 · Curvature of the Mind 2 on Genesis Framework · WordPress · Log in