Release Stats
New Simulations
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 Ο(r), projected 2D heatmap, and the iconic galaxy rotation curve where the observed flat velocity cannot be explained by visible mass alone.
Open simulation →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
π Brouwer: Pixel Heatmap + Grid Arrow Field
The canvas renders a full-resolution displacement heatmap
(createImageData), colored by HSL hue (direction) and
lightness (magnitude). A 24Γ24 grid of arrow vectors overlays the map
at sub-pixel precision. Fixed points are detected when
|f(x) β x| < 0.04 and marked with glowing β¦ stars. The
draggable contraction target introduces an interactive parameter:
moving the attractor immediately re-renders the heatmap and updates
the detected fixed point coordinates.
π Dark Matter Halo: NFW Physics
The NFW profile is Ο(r) = Οβ / [(r/rs)(1 + r/rs)Β²].
Enclosed mass follows
M(r) = 4ΟΟβrsΒ³[ln(1+r/rs) β (r/rs)/(1+r/rs)], and
circular velocity vc(r) = β(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.
πΈοΈ 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.