Hi,

I discovered “OpenSCAD” with the OpenSCAD contest.

Because its core is programming, I had to try implementing mathematical things.

Concept:

This openSCAD file makes use of “Fourier Transforms” which is a way of expressing any signal as a sum of cosine functions of different amplitude, intial phase and frequency.

There are a lot of great video about this operation. This video from 3B1B is excellent and is my inspiration for this project.

The concept of this model is to draw the result of a given sum of cosines as a 2D sculpture.

Two last parameters (Amplitude3D and Frequency3D) controls the geometry of the scuplture on the Z axis

Parameters:

There are 3 ways to control amplitude of the cosines:

• Manual policy : You can enforce a given amplitude for each cosine using the sliders.
• Enveloppe policy : You can enforce a maximum amplitude for each cosine using the sliders. The actual amplitude will be random between 0 and your max.
• FullRandom policy : Amplitudes are choosen randomly. Sliders are ignored.

There are 2 ways to control phases of the cosines:

• Manual policy : You can enforce a given initial phase for each cosine using the sliders.
• FullRandom policy : Initial phases are choosen randomly. Sliders are ignored.

The best combinaisons are:

• Manual for both policy if you want to understand the impact of each cosine or if you want to draw something in particular (a duck for exemple).
• Enveloppe for amplitude and FullRandom for phases if you want to generate some random art while enforcing a style

The Seed parameters is used to generate random parameters. Each seed will lead to a different sculpture. (If at least one of the policy isn't “manual”)

Tips:

By playing with the parameters, you will see that high frequencies (very negative or very positive) are responsible for sharp details of the sculpture whereas low frequencies (near 0) tend to smooth the sculpture.

Also, you will see that a sculpture based only on positive frequencies will look very different that sculpture that mixes negative and positive frequencies.

Printing and assembling:

It cannot be easier to print. No assembly.