01 / projects
Two identical double pendulums, released 0.001 rad apart. Chaos means the difference doesn't stay small.
Hamiltonian equations of motion integrated with fixed-step
RK4 at h = 2 ms. The faded trails belong to the second bob of each
pendulum. The HUD tracks the phase-space separation between the twins — once it
hits order 1, prediction is over.
The 1963 system that started modern chaos theory — with the three parameters on sliders.
Drop ρ below ~24.7 and the trajectory spirals into a fixed
point — the strange attractor only exists past the bifurcation. The classic
butterfly lives at σ=10, ρ=28, β=8/3. Slow rotation is just a
projection of the 3-D phase space, not physics.
The instantaneous field of two coherent point sources, computed per pixel every frame.
Each pixel evaluates
cos(k·d₁ − ωt) + cos(k·d₂ − ωt), squared for intensity. The static
fringe directions satisfy d·sinθ = mλ — count the bright lobes and
check. Rendered at half resolution and upscaled to stay smooth on phones.
More coming — write-ups of my Python work (orbital mechanics, data analysis) are next. The plumbing for them already exists; see the notes.