Toy Project Dynamics as Lenses — discrete brickwork + continuous slot sensor

This is a self-contained HTML demo (no external libraries) that treats (i) a discrete “cylindrical brick installation” as a state-transition system, and (ii) a continuous rotation observed through a viewing slot as an open dynamical system with a partial observation. The intent is proof-of-concept: state space, trajectories, and a lens-shaped interface (update/expose).

Brickwork: “blueprint filled in” as a deterministic/possibilistic transition system

Level 0: no restriction; Level 1: must alternate direction; Level 2: CW only. Each level adds curing delay.
“Step” advances by one brick placement or one curing tick.
Unwrapped cylinder: x = brick position (mod M), y = course index. Filled cells are placed bricks; yellow outline is the next brick.
Right panel sketches the unconstrained binary direction tree for the first few courses, highlighting the chosen feasible plan. Separate counts apply the current direction and start constraints; the reference tree does not filter forbidden branches.

Circular motion observed through a slot: a (differential) system + a sensor interface

Top: rotating point and the visible arc (slot). Bottom: visibility over time (white = visible).
Analytic visibility intervals
computed from θ(t)=θ₀+ωt mod 2π
Wiring diagram sketch
Init θ₀, ω, r ↦ s₀ Dynamics s=(θ,ω,r,τ), ṡ=update(s) expose(s)=(θ,r,τ) Slot sensor visible(θ), pos=(r cosθ, r sinθ) output=(vis,x,y,τ) Observation record Extract intervals (enter/exit times) from output stream state init θ,r,τ stream
Lens (Myers orientation) for the dynamics box

          

            In Myers’ convention, arenas are written (In/Out) with “inputs on top” and “outputs on bottom” so that expose is passforward and update is passback. (This is the flip of Spivak’s common (Out/In) display.)