Fractal design and analysis

Individually create a "new" fractal and analyze its fractal dimension.

Fractals are objects that display self-similarity with a never ending pattern that repeats itself at different scales. See What are Fractals? or Canvas > Content for more information.

I: Develop fractal

Create a fractal or modify an existing fractal to create something "new".

The goal is to create a new geometric fractal. "New" can be a modification of existing fractals as long as the original fractal is cited with a description of modifications. Possible ideas:

Once you have a possible idea, check to make sure that the fractal is not an copy of well-known fractals. Here are three possible searches to help: circles, squares, triangles

If you would like feedback, email the instructor pictures of the original shape and first iteration of the fractal rule.

II: Fractal on wikibook

Post separate images of the fractal.

  1. Show the first five images of the fractal on a single page. The five images include the starting shape then four iterations of the fractal rule.
  2. (optional) Give the fractal a cool name.

Possible tools for drawing fractals

III: Fractal dimension

Submit a paper that describes the fractal and justifies the fractal dimension.

Provide a clear definition for how the fractal is created. It may help to use transformations (dilation, translation, reflection about a line, rotation about a point) to give a precise definition.

Also compute the fractal dimension \(N = S^D\), where:

Each value should have some justification.

Possible resources


SUBMISSION

  1. (optional) Email to instructor for feedback.
  2. Images on wikibook. Please use unique names so files do not get overwritten.
  3. Submit a paper copy of the fractal's definition and dimension.

Scoring guide [20 MP]

Iterations

___ images or PDF clearly show fractal iterations.


Paper

Definition is ___ sufficient to create fractal without the aid of the images.

Justification for the fractal dimension _____

Fractal dimension is _____