Applied Science — Five New Categories for Engineering, Ecology and Combinatorics

Where We Are Now

Sessions 63 through 68 added fifteen new simulations across five newly established categories. Each category addresses a domain where simulation adds genuine insight beyond what text can convey: ecosystem dynamics, structural engineering, crop science, graph theory, and biological timekeeping. Here's the story behind each.

Category 1 — Ecology

Ecology sat on the TODO list for a long time. We had prey-predator (Lotka-Volterra agents) and SIR (epidemiology as a population model), but no dedicated ecology category that pulled them together. The missing piece was a multi-species food web and a trophic cascade simulation — the kind that illustrates the Yellowstone wolf story quantitatively, not just metaphorically.

The Food Web simulation runs six species (Grass, Shrubs, Rabbit, Deer, Fox, Wolf) on extended Lotka-Volterra equations with RK4 integration. The network graph where node size tracks population in real time is the payoff: you can watch the cascade propagate when you click a species off. The Trophic Cascade is a cleaner three-level system designed specifically to demonstrate top-down control — remove the carnivore, watch the herbivore population explode, watch vegetation collapse.

Category 2 — Civil Engineering

Civil engineering is one of the most simulation-intensive disciplines in real practice: finite element analysis drives every bridge, building, and dam design. Yet it was missing from our library. We launched the category with two simulations that target the most universally taught topics in undergraduate civil engineering curricula.

Beam Deflection implements the Euler-Bernoulli beam equation analytically: select beam type (simply supported / cantilever / fixed-fixed), loading (point load / UDL), material preset (steel / timber / aluminium / concrete), and see the deflection curve, bending moment diagram, and shear force diagram update in real time. The key formula is EI·d²y/dx² = M(x). Concrete Mix Design implements the ACI 211 method with Abrams' Law — the simulation that finally makes water-cement ratio intuitive.

Category 3 — Agronomy

Agriculture feeds the world, and agricultural simulation is a serious applied science. The DSSAT and APSIM modelling frameworks are used by agronomists globally to predict yield under climate scenarios, optimise irrigation timing, and model nutrient cycling. We don't replicate that complexity — but we do capture the core concepts at an accessible level.

Crop Growth uses the Growing Degree Day (GDD) model: crops advance through phenological stages as accumulated heat units cross thresholds. The simulation covers four crops (Wheat, Corn, Soybean, Sunflower), five growth stages each. Soil Erosion implements the RUSLE (Revised Universal Soil Loss Equation): A = R·K·LS·C·P, with animated rain and sediment transport canvases.

Category 4 — Combinatorics

Combinatorics had been a gap in our mathematics coverage. We had sorting algorithms, graph pathfinding, and the TSP — but nothing that sat squarely in discrete mathematics. Graph colouring is one of the most accessible hard problems in CS: the four-colour theorem, chromatic polynomials, and the connection to register allocation in compilers.

Graph Colouring implements three algorithms (Greedy / Welsh-Powell / DSatur) with step-by-step animation. Pascal's Triangle reveals the extraordinary density of mathematical structure hiding in a simple number grid: Fibonacci diagonals, powers of 2, Sierpiński fractal via parity colouring, binomial coefficients on hover. Both simulations are interactive — you can add nodes to the graph, drag them, and watch the chromatic number update.

Category 5 — Chronobiology

Chronobiology is the science of biological timekeeping. The 2017 Nobel Prize in Physiology or Medicine went to the discoverers of the molecular mechanism of the circadian clock — Hall, Rosbash, and Young. It felt wrong to have a simulation library without representing this.

The Circadian Rhythm simulation implements the Goodwin oscillator: a three-variable negative-feedback loop (mRNA → cytoplasmic protein → nuclear protein → repression of mRNA) that produces a ~24-hour cycle. The math is the same as the molecular CLOCK/BMAL1/PER/CRY loop. Presets explore jet lag, shift work, and the light-entrainment response.

Design Principles for "Applied Science" Categories

Each new category introduced in this sprint had to satisfy three criteria before we committed to it:

• Simulation adds value beyond text. A static diagram of trophic levels teaches less than a simulation where you click a predator out of existence and watch the cascade unfold over 200 simulated years. Civil engineering beam calculations exist as formulas in textbooks; seeing the deflection curve change shape as you move a load provides spatial intuition that the formula alone cannot.
• The core model fits in a Canvas 2D. We avoid simulations that require 3D rendering for their core insight. Concreteness over visual richness.
• The simulation has presets that tell a story. The soil erosion simulation isn't just a number — it's four presets that show the difference between a bare field and a forested slope. The concrete mix has presets tuned to common real-world mixes so users understand what the numbers mean.

What's Next

The applied science sprint revealed a long tail of teachable topics that still lack good interactive representations on the web. On our radar for the next wave:

• Hydrology — river discharge models, watershed runoff (SCS curve number), groundwater flow (Darcy's law)
• Operations Research — linear programming simplex tableau, assignment problem (Hungarian algorithm), vehicle routing
• Industrial Ecology — material flow analysis, LCA circular flow diagrams
• Geotechnical Engineering — soil consolidation (Terzaghi), slope stability (Bishop method)

In parallel, three existing categories are due for expansion: ecology (coral reef, ocean acidification–food web linkage), combinatorics (Ramsey numbers, generating functions), and civil engineering (retaining wall earth pressure, column buckling with Euler's formula). The goal remains the same as always: one genuinely insightful interactive simulation for every major concept in undergraduate science and engineering.

New Simulations This Sprint