A physics simulation of an inverted pendulum on a cart that evaluates three distinct control architectures—PID, LQR and MPC — on their ability to maintain equilibrium and recover from significant external disturbances.

For more videos click instagram.com/craftsandengineering, or tiktok.com/@zoomzoombee

For code click https://github.com/zombimann/Mathematical-video-animations-and-visualization/blob/main/The_Great_Pendulum_Balance_Off_PID_vs_LQR_vs_MPC.ipynb

An animation of the Feynman Path Integral, visualizing the Principle of Stationary Action.

For more videos click www.instagram.com/craftsandengineering

For code click Mathematical-video-animations-and-visualization/Feynman_Path_Integral_Visualization.ipynb at main · zombimann/Mathematical-video-animations-and-visualization

Inspired by this post on X https://x.com/scievision369/status/2055314591270436884?s=20

A high-quality animation of the Spiral of Theodorus (also known as the Pythagorean Spiral).

The animation illustrates the step-by-step construction of contiguous right triangles, providing both a visual and mathematical representation of irrational square roots.

For more videos click: www.instagram.com/craftsandengineering

For code click Mathematical-video-animations-and-visualization/Spiral_of_Theodorus_Geometric_Animation.ipynb at main · zombimann/Mathematical-video-animations-and-visualization

A high-fidelity, visually engaging animation illustrating the mathematical beauty and symmetry of inverse functions across the identity line

For more videos click www.instagram.com/craftsandengineering

For code click https://github.com/zombimann/Mathematical-video-animations-and-visualization/blob/main/Symmetry_of_Powers_and_Roots.ipynb

A high-fidelity 3D animation illustrating the fundamental geometric principles of Einstein's General Theory of Relativity.

For more videos click: www.instagram.com/craftsandengineering

For code click: https://github.com/zombimann/Mathematical-video-animations-and-visualization/blob/main/General_Relativity_Visualization.ipynb

An accurate 3D visualization of electromagnetic energy flow around a current-carrying conductor

For more videos click instagram.com/craftsandengineering/

For code click Mathematical-video-animations-and-visualization/Poynting_Vector_Wire_Energy_Flow_upgraded.ipynb at main · zombimann/Mathematical-video-animations-and-visualization

A high-fidelity algorithmic animation of four Pan-African and cultural icons using Weighted Voronoi Stippling. The process transforms standard grayscale images into dynamic stippled portraits where point density and size reflect the underlying image intensity.

For more videos click instagram.com/craftsandengineering/

For code click Mathematical-video-animations-and-visualization/Pan_African_icons_voronoi_stippling.ipynb at main · zombimann/Mathematical-video-animations-and-visualization

OFFER: Get a 2400×3000 converted version of your own portrait similar to these for $2. Send portrait to DM as well as any other specifications. I can only currently transact through MPESA.

This project provides a visual, 3D exploration of how a sphere's volume is constructed using calculus—specifically triple integrals in spherical coordinates.

For more videos click www.instagram.com/craftsandengineering

For code and more click Mathematical-video-animations-and-visualization/Sphere_construction_with_Triple_Integrals.ipynb at main · zombimann/Mathematical-video-animations-and-visualization

The Higgs Mechanism, electroweak symmetry breaking, and key particle physics concepts inspired by Feynman Diagrams.

Concepts visualized are:

The Higgs Field
Spontaneous Symmetry Breaking
Gluon Fusion
Higgs Decay to Photons (H → ̳̳)
The Golden Channel (H → ZZ → 4ℓ)
Electroweak Symmetry Breaking

For more animations click www.instagram.com/craftsandengineering

For code and more click https://github.com/zombimann/Mathematical-video-animations-and-visualization/blob/main/Quantum_Physics_Higgs_Mechanism_Feynman_Diagrams.ipynb

Music attribution: Quantum - PHNKR PHONK & Donovan on TikTok music library

A side-by-side comparison of various pathfinding and search algorithms on a randomly generated maze. Each algorithm is visualized to demonstrate its exploration strategy and efficiency in discovering the final path.

Algorithms Included

1. A*
2. Dijkstra
3. Greedy Best-First
4. BFS (Breadth-First Search)
5. DFS (Depth-First Search)
6. Bidirectional BFS
7. Weighted A*
8. Recursive Backtrack
9. Wall Follower

For more videos click www.instagram.com/craftsandengineering

For code and more click Mathematical-video-animations-and-visualization/maze_solvers_competition.ipynb at d39ad7e4143932582ce4cccdc89e3f5b7d69f417 · zombimann/Mathematical-video-animations-and-visualization

A generative art project that transforms mathematical equations into a high-definition (1080p) visual experience. By plotting diverse polar curves simultaneously in a synchronized grid, it creates a rhythmic 'dance' of geometry and light.

Visual Design

• Neon Aesthetic: Each curve is rendered using a 'Neon Stack'—a high-intensity core line layered over a soft, translucent glow to simulate light emission.
• Cinematic Palette: A curated set of vibrant colors (Cyan, Magenta, Lime, Gold, etc.) is assigned to different curve families to provide high contrast against the deep black background.
• Atmospheric Shimmer: A background particle field pulses with randomized alpha transparency, creating a sense of depth and cosmic atmosphere.

Gallery

The symphony features 12 distinct curves, including:

• Rose Curves (): Elegant symmetric patterns.
• Cardioids & Limaçons: Heart-shaped and looped trajectories.
• Spirals: Archimedean and Fermat variants that expand infinitely.
• Specialty Curves: The complex Butterfly curve and the infinite Lituus.

Technical Specifications

• Engine: Matplotlib Polar Projection.
• Resolution: 1920x1080 (Full HD).
• Frame Rate: 30 FPS.
• Encoding: H.264 MP4 via FFMpegWriter with a 3000kbps bitrate.

For more animations click www.instagram.com/craftsandengineering/

For code click Mathematical-video-animations-and-visualization/mathematical_polar_curves.ipynb at main · zombimann/Mathematical-video-animations-and-visualization

For other videos, click www.instagram.com/craftsandengineering.

This animation demonstrates additive color theory through a high-fidelity animation of a spinning Newton Disc.

Features

• Temporal Super-Sampling: Renders multiple sub-steps per frame to simulate realistic motion blur.
• Exponential Acceleration: Uses a non-linear speed ramp to simulate a motor starting up.
• Optical Blending: Shows how primary colors (RGB) merge into white when rotated at high speeds.
• MP4 Export: Includes code to render and download the final simulation.

For more animations, click www.instagram.com/craftsandengineering

For code, click Mathematical-video-animations-and-visualization/Newton_Disc_Color_Mixing_Simulation.ipynb at main · zombimann/Mathematical-video-animations-and-visualization

Quantum Physics Series

Video 1 of 6: Quantum Electrodynamics visualization using Feynman Diagrams

Author: Mugambi Ndwiga
In: www.instagram.com/craftsandengineering

This animation visualizes the fundamental interactions of Quantum Electrodynamics (QED) using Feynman diagram conventions. QED is the relativistic quantum field theory of electrodynamics, describing how light and matter interact.

Visualized Phenomena

The animation cycles through six key physical processes:

1. Compton Scattering: A photon hits an electron, resulting in an energy shift and change in direction.
2. Electron-Positron Annihilation: An electron and its antiparticle (positron) collide to produce high-energy photons ().
3. Pair Production: A high-energy photon interacts with the electric field of an atomic nucleus to create an electron-positron pair.
4. Bremsstrahlung (Braking Radiation): A charged particle (electron) is deflected by a nucleus and radiates energy as a photon.
5. Møller Scattering: The interaction and repulsion between two electrons via the exchange of a virtual photon.
6. Vacuum Polarization: A process where a photon temporarily fluctuates into a virtual electron-positron pair, affecting the vacuum's permittivity.

For code and more click Mathematical-video-animations-and-visualization/QED_Feynman_Diagrams_Animations.ipynb at main · zombimann/Mathematical-video-animations-and-visualization

A high-fidelity physics simulation of a Galton Board (also known as a Bean Machine).

For more click www.instagram.com/craftsandengineering/

A visually stunning animation of Harmonograph patterns—geometric drawings created by combining perpendicular oscillations.

For more click www.instagram.com/craftsandengineering