#fourier

While trying to program the curves produced by Spirograph toys in Grasshopper, I took a slightly different path. The topic eventually led to a broader heading: harmonic motion, and from there, to the Fourier Series we looked at previously. This simple Python code models Fourier Synthesis, driven by circles of different radii in a very straightforward way. The Python component sets up a loop that calculates the effect of each circle to the x and y values, individually. In this…

The Fourier Transform is a powerful mathematical technique that allows us to analyze the different frequency components within a signal or shape. Its discrete version, the Discrete Fourier Transform (DFT), is used when working with numerical data. I studied the Fourier Series here before. One of the most fascinating aspects of the DFT is that it can represent a signal or shape using rotating circles (or vectors). Each circle corresponds to a specific frequency, amplitude, and phase. When connected in…

This is my first experiment with the Fourier Series in Grasshopper using Python. This is a technique to decompose functions into their frequency components. Fourier series have a wide range of applications in physics and engineering. What makes it especially fascinating, however, is the visual intuition it offers. It looks like a kind of mathematical “magic” that emerges from the geometry of frequency. I explored several excellent visual explanations online, including those by Coding Train, 3Blue1Brown, and Mathologer, each offering…