Introduction
Can circles do more for us than draw these lovely patterns? Can they give us an alphabet, a universal way of generating and representing many forms of interest? Can we treat them like a bunch of kitchen ingredients, that we throw into a recipe to conjure up new dishes that look different?
Take a look at these paintings:
What is the Fourier Series?
Videos
How about the Euler Formula?
Rolling Circles and the Fourier Series
So, if we choose number of circles \(M\) and their complex amplitudes \(a_j\), \(j={1..M}\) relying on our (hopefully growing) intuition, we can systematically generate symmetric patterns based on the idea of rolling circles. By trial and error, we can design both the value of \(M\) and the values for \(a_j\), \(j={1..M}\). So far, so good.
But how about the other way around? What if we had a “pattern” in mind, and wanted to compute the circles, their number and amplitudes, that would generate that pattern? This is where the Fourier Series comes in.
- Alex Miler. (2018). Fourier Series and Spinning Circles. https://alex.miller.im/posts/fourier-series-spinning-circles-visualization/
Citation
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