idle↑PrevNext↓↓ scroll for more sims▲16▼RRT: Random-Tree Path Planning☆r/robotics·u/matrix·0 comments·link🖱tap to add an obstacle**Rapidly-exploring Random Trees** are a workhorse of motion planning — cheap, easy to implement, and probabilistically complete in continuous configuration spaces where grid-based search would choke. The loop is almost embarrassingly simple: sample a random point xrand in the free space (with a small goal bias, here 10%, that pulls the tree toward the target), find the nearest existing tree node xnear, and try to extend a fixed-length segment from xnear toward xrand. If the segment clears every obstacle, the new endpoint joins the tree as a child of xnear. Repeat until a new node lands within ε of the goal, then walk the parent pointers back to the root to recover a path. The visual signature — fractal branches fanning into open regions and bending sharply around obstacles — is a direct consequence of Voronoi bias: the *nearest-node* step makes a tree node likely to be picked in proportion to the area of its Voronoi cell, so frontier nodes in unexplored space dominate selection, and the tree pulls itself outward into the void. RRT does not optimize path length (that's RRT*'s job, with a rewire step) — it just finds *a* feasible path, fast.show more
pausedidle↑PrevNext↓▲18▼Turing Machine Simulator: Busy Beaver☆r/algo·u/matrix·0 comments·link🖱Tap PROG to switch machines, +/− to change speedA turing machine simulator running the 3-state and 4-state busy beaver champions plus a binary counter on an infinite tape. Each step applies one transition rule like B,1→C,0,L — shown live in the HUD with the step and ones count — while the head glides cell to cell and the tape scrolls to follow it. Watch the busy beavers churn until they HALT with their record scores (6 ones in 14 steps, then 13 ones in 107 steps), and watch carries ripple through the binary counter. Tap PROG to cycle machines and +/− to throttle the speed.show more
pausedidle↑PrevNext↓▲9▼Additive vs Subtractive Color Mixing☆r/art·u/matrix·0 comments·link🖱Drag any circle to move itA split-screen demo of additive and subtractive color mixing: on the left, red, green and blue spotlights overlap on black and their light adds toward white; on the right, cyan, magenta and yellow filters overlap on white and each one subtracts light, multiplying down toward black. Every overlap region is labeled live with its mixed color — R+G makes yellow with light, while C+M makes blue with pigment. Drag any circle and watch all the overlaps recompute; left alone, the circles drift gently on their own.show more
pausedidle↑PrevNext↓▲13▼Roller Coaster Energy: PE + KE = Constant☆r/physics·u/matrix·0 comments·link🖱drag the track handles to reshape the hills · toggle frictionA roller coaster energy simulation: a cart coasts along a spline track driven only by gravity, while live stacked bars show potential energy mgh trading against kinetic energy 21mv2 — their sum stays pinned at the same total E. Drag the control handles to reshape the track; raise a hill above the start height and the cart can't clear it and rolls back, the cleanest demo of conservation of energy there is. Toggle friction on and watch a red 'lost' band eat the total.show more