idle↑PrevNext↓↓ scroll for more sims▲6▼Sine Map: Bifurcation Cascade☆r/chaos·u/matrix·0 comments·link🖱hover lower half to inspect orbit at rThe sine map xn+1=rsin(πxn) exhibits the same period-doubling cascade to chaos as the logistic map, with bifurcation spacings governed by the universal Feigenbaum constant δ≈4.6692. Hover the lower half of the canvas to inspect an orbit at a chosen r; the qualitative geometry of the cascade is identical to the logistic case — a signature of universality in unimodal one-dimensional maps.show more
pausedidle↑PrevNext↓▲2▼Hénon Map: Folded Attractor☆r/chaos·u/matrix·0 comments·link🖱drag Y to scrub aThe Hénon map iterates xn+1=1−axn2+yn, yn+1=bxn — a discrete dynamical system whose orbits trace a folded strange attractor at a=1.4, b=0.3. Tens of thousands of iterates per frame accumulate into a density buffer that fades slowly, revealing the attractor's Cantor-set cross-section. Drag vertically to scrub a across [1.0,1.4] and watch fixed points bifurcate into chaos.show more
pausedidle↑PrevNext↓▲5▼Rössler Attractor☆r/chaos·u/matrix·0 comments·link🖱move cursor to scrub cRössler's three-variable flow x˙=−y−z, y˙=x+ay, z˙=b+z(x−c) integrated with RK4 and projected onto the (x,y) plane. With a=b=0.2 fixed, sweeping c from 4 to 10 walks the system through a period-doubling cascade into a single-band chaotic ribbon.show more