To do:

Kalman Filter

Tidy things up

Reaction Diffusion Equation and Pattern Formation

Probabilistic Relational Agent Models

Functional Agent-based Models

GLMs

Power and statistical errors in relation to sample size

Relationships between Probability Distributions

Wave front expansion -> Tree front expansion?

Chaos Theory and Fractals: Simulation: Implement the logistic map or the Mandelbrot set. Visualization: Create color-coded plots to show the chaotic behavior and fractal structures. The Mandelbrot set, in particular, can produce stunningly intricate visualizations.

Agent-Based Models in Ecology or Economics: Simulation: Create an ecosystem with different species interacting or a market model with agents having different economic behaviors. Visualization: Use animated plots to show how the system evolves over time, or network diagrams to illustrate the interactions between agents.

Monte Carlo Simulations: Simulation: Use Monte Carlo methods to model phenomena like stock price evolution, weather patterns, or nuclear reactions. Visualization: Generate histograms, scatter plots, or line plots to show probability distributions, correlations, and trends.

Heatmaps of Matrix Operations: Simulation: Perform complex matrix operations or linear algebra computations. Visualization: Use heatmaps to represent the matrices, showing the magnitude of elements with color intensity.

Solar System Simulation: Simulation: Model the motion of planets in a solar system using Newtonian mechanics. Visualization: Create 2D or 3D animations showing the orbits of planets, potentially highlighting phenomena like retrograde motion.

Wave Propagation and Interference: Simulation: Simulate wave propagation in mediums, interference patterns, or the double-slit experiment. Visualization: Use contour plots or animated plots to show wave dynamics and interference patterns.

Cellular Automata and the Game of Life: Simulation: Implement Conway's Game of Life or other cellular automata. Visualization: Generate grid-based visualizations showing the evolution of the automaton over time.

Fluid Dynamics and Smoke Simulation: Simulation: Model fluid flow or smoke using Navier-Stokes equations. Visualization: Use color gradients in animations to effectively represent fluid or smoke movement and density.

Disease Spread Simulation (Epidemiology): Simulation: Model the spread of a disease using a SIR (Susceptible, Infected, Recovered) model or more complex variants. Visualization: Create maps showing the spread of the disease, or line/bar graphs to represent the change in population states over time.

Neural Network Training Visualization: Simulation: Train a simple neural network on a dataset. Visualization: Show how weights and biases change over time, or plot the decision boundary evolution as the network learns.