Devlog #25 — Spring 2027: 345 Simulations, Relativity Category, Ecology and Mathematical Biology

The Numbers

345

Interactive simulations

75+

Subject categories

30+

New sims this quarter

345 simulations span topics from quantum tunnelling and Grover's algorithm all the way to soil erosion models and concrete mix design. Every simulation ships with EN and UK (Ukrainian) language versions, structured JSON-LD metadata, and a category page entry. The sitemap now lists over 1 360 URLs.

Headline Addition: Special Relativity

The relativity category launched this quarter with six interactive simulations covering special and general relativity. Together they form a complete self-contained course on the geometry of spacetime — from the basic Lorentz factor to E = mc² and gravitational lensing.

Why build a full relativity category? Special relativity is taught in most physics curricula but rarely visualised interactively. Spacetime diagrams are the natural language for understanding time dilation and length contraction — but most students never work with them. Our Minkowski diagram lets you drag a velocity slider and watch simultaneity planes tilt in real time, which resolves most "paradoxes" instantly.

Mathematics: Topology, Series and Number Theory

The mathematics category expanded with several new simulations bridging visual intuition and rigorous concepts:

Möbius Strip 3D parametric surface, depth-sorted Phong shading, ant-path animation proving single-sidedness, twist count 1–5 with sides/edges counter. Taylor Series 8 functions (sin/cos/exp/ln/arctan), animated term addition, error plot, convergence radius — term coefficients displayed live. Collatz Conjecture 3 views: animated log-scale sequence, stopping-time heat map, reverse tree depth ≤8. Includes the infamous n=837799 preset. Pascal's Triangle Rows 3–20, 3 colour modes (log, parity/Sierpiński fractal, mod-N palette), Fibonacci diagonal highlight, C(n,k) hover formula. Riemann Integral Left/right/midpoint/trapezoid/Simpson rules; 7 functions; live approximation, exact value, and error with ≤200 subdivisions. Matrix Transforms 2D 4 sliders a/b/c/d (−3..+3), 8 presets, eigenvectors, unit circle, trace/det/λ₁/λ₂, matrix type indicator.

Ecology & Life Sciences

Two new ecology simulations launched alongside expanded cell biology and genetics coverage:

Food Web Dynamics 6-species ecosystem (Grass→Rabbit→Fox chain, Shrub→Deer→Wolf). Extended Lotka-Volterra + RK4. Network graph + time series. Click to toggle species extinction. Trophic Cascade 3-level Lotka-Volterra: plants → herbivores → predators. Toggle predator removal to observe classic "trophic cascade" effect on vegetation. Osmosis & Plant Cell Animated plant cell with vacuole, 50 water molecules, solute particles. Turgor pressure, volume graph. 5 presets: hypotonic through plasmolysis. Mitosis & Meiosis 7-phase mitosis and 10-phase meiosis with phase chips, play/step controls, spindle fibres, nuclear envelope, cleavage furrow.

Earth & Atmospheric Science

Aurora Borealis 180 spiralling charged particles follow dipole field lines. Green O (100–150 km), red O (200–300 km), violet N₂ (70–100 km) emission bands. Kp-index slider. Glacier Dynamics 1D shallow-ice Glen's flow law, 200 cells, ELA-based mass balance. Temperature anomaly/snowfall/slope sliders. Ice body canvas + length time series.

Engineering & Applied Science

Three new applied/engineering simulations launched this quarter, completing civil-engineering and agronomy category foundations:

Concrete Mix Design ACI 211 mix design + Abrams' law f'c = A/B^(w/c). 4 cement types, w/c ratio, aggregate sliders, strength curve, slump cone, mix proportion bar. Beam Deflection Euler-Bernoulli beam: simply-supported/cantilever/fixed-fixed, point/UDL loading, 3 sub-plots (deflection/moment/shear), Steel/Wood/Aluminium/Concrete presets. Soil Erosion (RUSLE) RUSLE model A=R×K×LS×C×P. Canvas soil layers + rain animation + sediment transport. 4 presets: bare soil, row crop, pasture, forest.

Algorithms & Combinatorics

N-Queens Problem Backtracking step-by-step on 4–12 board. Colour-coded active (yellow), placed (green), conflict (red), and solution (blue) queens. Stats: solutions/backtracks/steps. Graph Colouring Chromatic number χ(G): Greedy/Welsh-Powell/DSatur algorithms. Petersen/K₅/cycle/bipartite/wheel/random presets, step-by-step mode, conflict highlighting.

Spiral Mathematics in Ukrainian (Flat-Path)

Two standalone simulation pages were added as Ukrainian canonical flat-path URLs, reflecting a design choice to make the Ukrainian versions first-class citizens rather than subpages:

uk/fibonacci/ — Fibonacci Spiral: 3 modes (🌀 Spiral / 🌻 Sunflower / ⬛ Squares), golden angle 137.5°, point-count/angle/size sliders, 4 colour schemes, full-screen canvas, PNG export.
uk/moon-phases/ — Moon Phases: 8 phase chips, day 0–29.5 slider, play/pause with speed control, orbital animation (Earth+Moon+Sun+stars), crescent/gibbous algorithm, phase/illumination/cycle-day statistics.

What's Next

The roadmap for Q2 2027 centres on three themes:

Plasma physics category — Tokamak confinement, Debye shielding, Kelvin-Helmholtz instability, and Z-pinch simulations are in development.
Topology — Beyond the Möbius strip: Klein bottle, knot theory invariants, hyperbolic disk geometry.
Data science hub — PCA, decision trees, neural network backpropagation visualiser, and a Bayesian inference workbench.
Blog expansion — The Learning series continues with #15 (probability and inference) and #16 (ecology and ODEs); a new Educator Stories post is in progress.

EN + UK parity maintained at 100%. Every simulation ships with both an English and a Ukrainian version. The sitemap currently lists 1 364 URLs — nearly all are EN/UK pairs. The Ukrainian versions are canonical (not just translations): they use Ukrainian scientific terminology and Ukrainian-specific examples where applicable.