Bio-Inspired AI & Optimization – Course Visualizations
Supplemental visualizations for Theodore Pavlic's IEE/CSE 598: Bio-Inspired AI and Optimization at Arizona State University.
Lectures and other helpful short video tutorials can be found at TedPavlic's YouTube channel.
© 2026 Theodore P. Pavlic · MIT License
Genetic Algorithms
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Shifting Balance Theory – interactive explainer
Walk through Sewall Wright's three-phase Shifting Balance Theory: how genetic drift, selection, and interdemic migration help a metapopulation escape local fitness peaks.
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Ideal Free Distribution – interactive explainer
Watch animals distribute across resource patches to equalize individual fitness – a behavioral ecology result that motivates fitness sharing in multi-modal genetic algorithms.
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Evolution as Movement in a Drift Field – graphical explainer
Selection and drift purge diversity; mutation replenishes it. This figure frames the four forces of evolution as a field pushing populations toward fixation, motivating how to tune GA hyperparameters for a gradual shift from exploration to exploitation.
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Genetic Algorithm Explorer – interactive explainer
Run a canonical GA on a 1-D multimodal landscape with niching, experiment with an island model / distributed GA, explore a 2-D optimization zoo, and watch a two-objective MOEA build a Pareto front in real time.
Evolution Strategies
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ES Explorer – interactive explainer
Run a (μ,λ)- or (μ+λ)-Evolution Strategy on a 1-D multimodal landscape and watch per-individual step sizes self-adapt through selection – no global update rule required.
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CMA-ES Explorer – interactive explainer
Watch CMA-ES adapt its mean, step size, and full covariance matrix each generation – cumulative step-size adaptation and rank-1/rank-μ covariance updates visualized in real time on a 2-D landscape.
Evolutionary Programming & Artificial Immune Systems
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Evolutionary Programming Representations – interactive explainer
Explore Abstract Syntax Trees, Linear Genetic Programs, and Finite-State Machines side by side – interact with each representation, apply variation operators, and compare their expressiveness and typical applications.
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Artificial Immune Systems Explorer – interactive explainer
Explore Negative Selection (NSA) and CLONALG side by side – watch detectors train on self-data to flag anomalies, and see how clonal selection and affinity maturation build a pattern-recognition repertoire.
Physics-Inspired Methods
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Monte Carlo Explorer – interactive explainer
Estimate π by dartboard sampling and by dropping Buffon’s needles, measure a floor area from the crossings of a robot’s own trails the way a nest-seeking ant may size up a cavity, and integrate a function by averaging random draws, running repeated experiments to watch 95% confidence intervals accumulate around the true value.
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Simulated Annealing – interactive explainer
Step through the annealing process: temperature schedules, neighbor selection, and probabilistic acceptance criteria on an energy landscape.
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Parallel Tempering / REMC – interactive explainer
Run parallel fixed-temperature SA replicas at different temperatures and periodically swap configurations between them – high-temperature replicas explore globally while low-temperature ones refine solutions.
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Softmax Temperature Explorer – interactive explainer
Adjust the temperature of the softmax (Gibbs) distribution and watch how it interpolates between uniform exploration and greedy exploitation – the same mechanism underlying SA acceptance and MaxEnt methods.
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Maximum Entropy (MaxEnt) – interactive explainer
Explore how the Maximum Entropy principle selects the least-assumptive distribution consistent with known constraints – and how this derivation produces the Gibbs/softmax distribution that underlies SA acceptance probabilities.
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Boltzmann Distribution via Random Exchange – interactive explainer
N agents repeatedly trade random amounts of a conserved quantity – watch any starting distribution relax to the maximum-entropy Boltzmann (exponential) equilibrium, confirming the statistical mechanics origin of the Gibbs distribution.
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Beta Distribution Explorer – interactive explainer
Adjust α and β to reshape the Beta(α,β) distribution, draw N samples, and watch how their order statistics and spacings reveal the deep connection between uniform random variables and the Beta distribution.
Swarm Intelligence
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Boids Explorer – interactive explainer
Tune separation, alignment, and cohesion weights in Reynolds' Boids model to watch emergent flocking arise from three simple local rules – a classic model of collective motion that inspired swarm intelligence algorithms like PSO.
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Vicsek Model Explorer – interactive explainer
Adjust noise and interaction radius in the Vicsek model to watch self-propelled particles transition between disordered flocking and coherent swarm behavior – a minimal model of collective motion in biological and robotic swarms.
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Particle Swarm Optimization (PSO) Explorer – interactive explainer
Step through the PSO velocity-update rule – inertia, cognitive, and social components – then run a live swarm on a 2-D landscape and watch particles collectively converge on optima.
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Bacterial Foraging Optimization (BFO) Explorer – interactive explainer
Run the complete Bacterial Foraging Optimization algorithm (Passino 2002): experiment with cell-to-cell attractant/repellent signaling and tumble-swim chemotaxis in 1-D and 2-D, then step through the full nested loop – chemotaxis, reproduction, and elimination-dispersal – to watch a swarm collectively locate optima.
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ACO / Ant System Explorer – interactive explainer
Watch a pheromone-guided ant colony tackle a layered combinatorial problem and a Travelling Salesman Problem – adjust evaporation rate, deposit scale, and exploitation bias to see how stigmergic reinforcement drives collective search.
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Ant Foraging Dynamics Explorer – interactive explainer
Explore how ants collectively select foraging trails through pheromone stigmergy: experiment with trail noise and Y-maze decision-making, then see how recruitment linearity shapes collective path selection.
Neural Networks
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Single-Layer Perceptron – Neuron & Lever Explainer
Animated connection between the biological neuron and the linear classifier – adjust synaptic weights and inputs to watch the decision boundary shift in real time.
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Radial Basis Function Neural Network – interactive explorer
Adjust centers, widths, and weights of radial kernels to see how an RBF network builds up an approximation – making the hidden-layer geometry of this bio-inspired architecture tangible.
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Multi-Layer Perceptron & Backpropagation – interactive explorer
Explore how hidden layers let a network solve XOR and other non-linearly separable tasks, and trace backpropagation as gradient flow through the network's architecture.
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Cross-Entropy – An Information-Theoretic View – interactive explainer
Step from logit scores through softmax and entropy to cross-entropy loss and binary BCE – building the information-theoretic foundation behind neural network classification one concept at a time.
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MVT Explorer – Marginal Value Theorem – interactive explainer
Drag the tangent line to find optimal patch residence times under Charnov's Marginal Value Theorem – and see how the habitat-wide rate R* functions as an opportunity cost of time, mirroring the temporal discount rate in the reinforcement learning Bellman equation.
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Autoencoder Explorer – interactive explainer
Train a deep autoencoder on MNIST-like digit data and watch the 2-D bottleneck encoding cluster by class – a hands-on demonstration of unsupervised representation learning with neural networks.
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Recurrent Networks & Temporal Supervision Explorer – interactive explainer
Trace the evolution from Time-Delay Neural Networks to RNNs with output feedback and autoregressive latent-state RNNs, train them via Backpropagation Through Time (BPTT), and follow a visual guide to gated architectures (LSTM, GRU) that solve the vanishing-gradient problem.
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Reservoir Computing – Echo State Network Explorer
Adjust spectral radius, sparsity, and input scaling to watch a fixed random reservoir project inputs into a high-dimensional state space where a simple linear readout can separate complex dynamics – the key insight of reservoir computing via Echo State Networks.
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RMS Voltage – Power Dissipation Explorer – interactive explainer
Switch between sine, square, triangle, and sawtooth waveforms to see how RMS voltage depends only on waveform shape and equals the DC voltage that dissipates the same power – building signal-energy intuition that underpins reservoir state analysis.
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Transformer Architecture Explorer – interactive explainer
Step through scaled dot-product self-attention, multi-head attention, positional encodings, and Vision Transformers (ViT) with live attention-map and patch-embedding visualizations.
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Toward Multimodal AI – interactive explainer
Trace the path from CNNs and patch embeddings to Vision Transformers, CLIP-style contrastive pretraining, and modern multimodal architectures – showing how a single attention mechanism unifies vision and language.
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Spiking Neural Networks – interactive explorer
Simulate leaky integrate-and-fire neurons, visualize spike trains and membrane potentials, and explore Spike-Timing-Dependent Plasticity (STDP) – the biologically plausible Hebbian learning rule linking neural firing timing to synaptic weight changes.
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Ferroelectric Memristor Synapses & Crossbar Learning – interactive explainer
Explore how ferroelectric memristor synapses in a crossbar array implement Spike-Timing-Dependent Plasticity (STDP) – adjust pulse timings, device parameters, and network architecture to watch Hebbian learning emerge from nanoscale physics.
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Hebbian Learning & Competitive Clustering – interactive explainer
Explore how Hebbian synaptic update rules combined with lateral inhibition drive winner-take-all competition, organizing input patterns into distinct clusters without supervision – bridging the STDP memristor demo to classical unsupervised ANN learning.
Cellular Automata
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ECA Explorer – Elementary Cellular Automata
Explore all 256 of Wolfram's elementary cellular automaton rules: pick a rule, seed the first row, and watch how simple local update logic generates everything from simple repetition to complex, seemingly random patterns.
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Voter Model & Consensus Dynamics – interactive explainer
Watch cells adopt their neighbors' opinions through local copying rules – and see how a simple stochastic CA reaches consensus, coexistence, or fragmentation depending on network structure and update rules.
More from Ted Pavlic
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Simulating Stochastic Systems – Course Visualizations
Supplemental visualizations for a separate ASU undergraduate course on simulating systems driven by randomness: random variate generation, discrete-event simulation, queueing, and output analysis.
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Topic Visualizers – Interactive Explainers
Interactive web demonstrations across science, mathematics, statistics, and engineering.
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Notes, Documents, & Guides
Markdown-formatted notes and instructional guides on a variety of fundamental and applied science and engineering topics.
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Lectures and short video tutorials on YouTube
Including the Office Hours playlist.