# Nonlinear Systems- 12 Fractals

We have encountered many extraordinary phenomena during this course but fractals may top them all, self-similar geometric forms that repeat themselves on various scales, they can both contain infinite detail as we zoom in and the very counter intuitive phenomena of infinite length within a finite form, with all of this being the product of very simple iterative rules.

For full courses, transcriptions and downloads please see: http://www.complexityacademy.io

Transcription excerpt: Fractals are sometime called the pictures of nature and if chaos theory, as the name implies, is the chaotic and unpredictable dimension to nonlinear systems then we might say fractals represent their orderly side. We see lots of order in our world, the earth goes round the sun today and it will do the same tomorrow and the next day for millions of years, if we take a butterfly we see that one side of it is almost exactly mirrored in the other, we see the same in the regular geometric forms of snowflakes. One way of understanding this order is through the concept of symmetry. In mathematics, "symmetry" can be defined as an object or process that is invariant to a transformation, in more familiar terms, this means something that stays the same despite a change. So with our example of the butterfly, its external physiology had a reflection symmetry meaning we can simply flip one side over and we will get the other, the same was true of our snowflake and we could imagine some symmetry in the pattern…

- Kind: Short
- Year: 2015
- Runtime: 6 min
- By: Complexity Academy
- Genres: Science
- Archive: [Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Nonlinear_Systems-_12_Fractals.webm)
- Licence or status: [CC BY 3.0](https://creativecommons.org/licenses/by/3.0) (as the archive states it)
- Credit: Complexity Academy
- Who can watch: Tweens profiles and older (the archive gives no rating; placed by Invisible Network from its collection and subjects)

[Watch now](https://invisiblenetwork.ai/watch/archive/commons/58002393?play=1)