Release Stats
New Simulations
Gyroscopic Precession
3D projection of a spinning gyroscope on a pivot. Shows the precession cone traced by the axis tip, with angular velocity Ļ, torque Ļ = r Ć mg, and precession rate Ī© = mgr/(IĻ) calculated live. Adjust spin speed, tilt angle, and rotor mass.
Open simulation →Magnetic Hysteresis
Interactive B-H loop with magnetisation and applied field. Traces the full hysteresis cycle showing saturation magnetisation, remanence (remnant B at H=0), and coercivity (H needed to demagnetise). Switch between hard and soft magnetic materials.
Open simulation →Sand-Pile Criticality
Drop sand grains one by one onto an Abelian sandpile grid. When a cell reaches the critical slope, it topples and triggers cascading avalanches that follow a power-law size distribution ā a defining feature of self-organised criticality.
Open simulation →Technical Highlights
š Precession: Angular Momentum in 3D
The precession simulator uses a 3D-to-2D isometric projection to
render the gyroscope axis and precession cone. The key physics
relationship is Ī© = mgr / (IĀ·Ļ) where Ī© is
the precession angular velocity, m is the rotor mass,
g is gravity, r is the
pivot-to-centre-of-mass distance, I is the moment of
inertia, and Ļ
is the spin angular velocity.
The simulation accumulates the precession angle each animation frame:
Ļ += Ī© Ā· dt, then rotates the spin axis vector around the
vertical using a rotation matrix. The 3D tip trajectory traces the
precession cone, and the rotor is drawn as a perspective-projected
ellipse. Nutation (wobbling) is omitted for clarity ā the simulator
shows ideal torque-free precession with a steady cone.
Counterintuitive result: increasing spin speed Ļ decreases precession rate Ī© (Ī© ā 1/Ļ). Students can verify this by dragging the spin slider from maximum down to minimum and watching the precession cone widen and accelerate.
š§² Hysteresis: Nonlinear B-H Physics
The B-H loop is modelled using the Jiles-Atherton framework simplified to a smooth sigmoid saturation curve with memory. The loop is parameterised by three physical quantities: saturation magnetisation B_sat (maximum B achievable), remanence B_r (B remaining when H = 0 on the return branch), and coercivity H_c (the reversed field needed to bring B back to zero).
The simulation sweeps H sinusoidally and traces B in real time on a Canvas plot. Soft magnetic materials (e.g. iron) show narrow loops (low H_c, low energy loss), while hard materials (e.g. NdFeB permanent magnets) show wide loops with high coercivity ā this is what makes them useful as permanent magnets. The enclosed loop area is proportional to the energy dissipated per cycle as heat.
šļø Sand-Pile: Self-Organised Criticality
The Abelian sandpile model (Bak, Tang & Wiesenfeld, 1987) operates on an NĆN grid. Each cell holds an integer grain count. A cell is stable if its count is less than the critical threshold (4 for a square lattice). When a cell reaches the threshold, it topples: it loses 4 grains and each of its four neighbours gains 1. Toppling propagates until all cells are again stable ā the resulting cascade is an avalanche.
The simulator counts grains in each avalanche and builds a log-log
histogram of avalanche sizes. For large grids at the critical state,
this histogram converges to a straight line ā evidence of a power law
P(s) ā sā»įµ with exponent Ļ ā 1.2 for the 2D square
lattice. The system self-organises to this critical state without any
external tuning of a control parameter, which is the defining property
of SOC.
What's Next
Wave 42 is already in progress and will focus on cell biology and immunology topics. The TODO backlog also identifies several highly requested simulations: a Hall Effect follow-up showing the quantum Hall regime, a Lorenz Attractor in full 3D, and deeper dives into Nuclear Physics including binding energy curves and fission chain reactions. Community suggestions welcome on the Contribute page.