Fractals & Chaos Recap for 12/13

We then introduced our next Very Important Program: Complex Paint. This software was created by former F&C students Devon Loehr and Connor Simpson, updating software originally available only on MacOS9, and will be invaluable to us going forward. We’ll discuss the features of the program as they become relevant, but after downloading/unzipping the folder listed in the Google Drive folder linked, read the README file for help on how to use the software.

For now, we are using “Linear” mode, and working off of Complex Paint Worksheet 1. We’ve observed that in the linear complex expression Az+B, the value of A can affect the type of fixed point we get. For example, the angle of A written in polar form seems to govern the number of spokes we get, and the attracting/repelling/neutral nature of the fixed point is tied to the value of r. The value of B seems to just change its location. We’ve also noticed some unusual differences in the patterns we see: sometimes the path of attraction towards a fixed point forms straight-line spokes, but sometimes it forms spirals instead. Odd…

We’ll have to look at this some more going forward!

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