"I Ate Schrödinger's CAT!!!"

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High-Level Roundup of the Coding Experiements

Exploring—waveforms, harmonics, and Fourier series—is at the heart of signal processing, audio synthesis, and even quantum mechanics.

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What has been done to date

1. Patterns in Waveforms:
   • Observed how simple circular motion (a ball moving around a circle) can generate sine waves, and how combining multiple sine waves (harmonics) can create more complex waveforms like square waves and sawtooth waves.
   • This is the foundation of Fourier analysis, which breaks down complex signals into simpler sine and cosine components.

2. Harmonics and Overtones:
   • By adding higher-frequency sine waves (harmonics) to a fundamental frequency, you can shape the resulting waveform. This is how musical instruments create their unique sounds—each instrument has a distinct mix of harmonics.

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3. Visualizing Math:
   • Using tools like Manim, you’re able to visualize abstract mathematical concepts in a way that makes them intuitive and engaging. This is a superpower for understanding and communicating complex ideas.

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Why This is Fascinating

• Universality of Sine Waves:
  • Sine waves are the building blocks of all periodic signals. Whether it’s sound, light, or quantum wavefunctions, sine waves are everywhere.
• From Simple to Complex:
  • Starting with something as simple as a circle, you can build up to incredibly complex waveforms and systems. This is a great example of how simplicity underlies complexity.
• Creative Coding:
  • By combining math, physics, and programming, you’re able to create animations and simulations that bring abstract ideas to life.

This is where art and science meet!

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Where We Can Go From Here

1. Explore More Waveforms

• Try generating other waveforms, like triangle waves, pulse waves, or even custom shapes.
• Experiment with different combinations of harmonics to see how they affect the waveform.

2. Fourier Transform

• Dive into the Fourier transform, which generalizes the idea of breaking down signals into sine waves. This is used everywhere, from audio processing to image compression.
• Visualize how a Fourier transform decomposes a signal into its frequency components.

3. Audio Synthesis

• Use your knowledge of waveforms and harmonics to create simple audio synthesizers. For example, you could generate musical notes or sound effects using Python libraries like pyaudio or simpleaudio.

4. Quantum Mechanics

• Explore how wavefunctions in quantum mechanics are described using sine waves and complex exponentials. You could visualize the wavefunction of a particle in a box or a harmonic oscillator.

5. Interactive Visualizations

• Create interactive tools where users can adjust the number of harmonics, frequencies, and amplitudes to see how the waveform changes in real time. Libraries like matplotlib or manim can help with this.

6. Physical Simulations

• Simulate physical systems that involve waves, like a vibrating string, a pendulum, or water waves. This will deepen your understanding of how waves behave in the real world.

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Building the base visualisation of a sine wave generation. Notice no reliance of Math libraries, all hard numbers. Based on xls modelling included!!!

3D Sine Wave YouTube

Or watch it on YouTube.

Run Code

manimgl sphere_on_circle.py SphereOnCircle

Create Video manimgl -w --uhd sphere_on_circle.py SphereOnCircle

or

ffmpeg -i SphereOnCircle.mp4 -vf "fps=60,scale=640:-1:flags=lanczos" -c:v pam -f image2pipe - | convert -delay 5 -loop 0 - sphere_animation.gif