With modern day computers it is an easy task to approximate fractals. The type of fractal which ranks the highest on the easy-scale are probably fractals generated by functions in the complex plane. In almost any programming language (with a plot package) this will only take you a few lines of code. Even though it is just a simple task it is fun work because even if you insert a simple function you can get vastly complicated output. So I call my next math art:
Easy complex fun
How it was made: This picture is in some sense generated by finding the roots of this function:
The above function has three roots (one with zero imaginary component and the other two with non-zero real and imaginary part) . I compute the roots by using the Newton method. If you feed the Newton method a point in the complex plane then it can converge to one of the roots (note that it also can diverge). I gave every point which converges to the same root the same color and then you get the pretty picture above.
Things to ponder: When looking at the boundary of the colored regions you see that all three colors meet. What does this say about the boundary?
Sources: Formula rendered using Quicklatex -> http://quicklatex.com/
Updated: I added the steemstem-tag since some steemstem members gave me the green light on this.
Owl tax
Photo by Albrecht Fietz - Pixabay- CC0 Creative Commons
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