Devlog #63 – Wave 43: Topology & Cosmology Trifecta

Wave 43 crosses two of physics' most abstract frontiers in a single release: pure mathematics via the Brouwer Fixed Point Theorem, and large-scale astrophysics through Dark Matter Halo density profiles and Cosmic Web filament formation. All three launch with full Ukrainian translations, bringing the platform to 502 simulations.

Release Stats

502
Total simulations
63
Devlog entries
43
Release waves
2
New categories

New Simulations

πŸ“

Brouwer Fixed Point Theorem

Every continuous self-map of a disk has at least one fixed point. Five map types (Contraction, Rotation, Squeeze, Twist, Antipodal) β€” with a displacement heatmap and auto-detected fixed points. Draggable target for the contraction map.

Open simulation →
🌌

Dark Matter Halo β€” NFW Profile

Visualize the Navarro-Frenk-White (NFW) density profile ρ(r), projected 2D heatmap, and the iconic galaxy rotation curve where the observed flat velocity cannot be explained by visible mass alone.

Open simulation →
πŸ•ΈοΈ

Cosmic Web

N-body gravitational clustering with density-dependent force and comoving expansion. Watch particles form voids, filaments, and cluster nodes β€” the large-scale structure of the Universe.

Open simulation →

Technical Highlights

πŸ“ Brouwer: Pixel Heatmap + Grid Arrow Field

The canvas renders a full-resolution displacement heatmap (createImageData), colored by HSL hue (direction) and lightness (magnitude). A 24Γ—24 grid of arrow vectors overlays the map at sub-pixel precision. Fixed points are detected when |f(x) βˆ’ x| < 0.04 and marked with glowing ✦ stars. The draggable contraction target introduces an interactive parameter: moving the attractor immediately re-renders the heatmap and updates the detected fixed point coordinates.

🌌 Dark Matter Halo: NFW Physics

The NFW profile is ρ(r) = ρ₀ / [(r/rs)(1 + r/rs)Β²]. Enclosed mass follows M(r) = 4πρ₀rsΒ³[ln(1+r/rs) βˆ’ (r/rs)/(1+r/rs)], and circular velocity vc(r) = √(GM(r)/r). The split panel shows the projected 2D colour map on the left and the rotation curve on the right, distinguishing stellar, dark matter, and total observed components with dashed and solid lines.

πŸ•ΈοΈ Cosmic Web: N-body + Expansion

A simplified but physically motivated N-body simulation: particle positions in comoving coordinates, gravitational force softened at short range, and a Hubble-like expansion term that stretches void regions. The result qualitatively reproduces the cosmic web topology β€” voids, sheets, filaments, and nodes β€” that emerges in full cosmological hydro-simulations like IllustrisTNG.

Categories Growing

Wave 43 adds the first simulation to the topology category (Brouwer) and expands cosmology with two new entries. The cosmology category now covers: Big Bang Nucleosynthesis, CMB spectrum, Black Body Radiation, Dark Matter Halo, and Cosmic Web.

topology cosmology fixed-point dark-matter NFW-profile N-body rotation-curves
← Devlog #62 (Wave 42) Devlog #64 (Wave 44) →