Rotation is real.
Awareness is a hypothesis.
Two mathematical states in 90° quadrature. Freeze their logical time, preserve a checkpoint, and examine what can — and cannot — be inferred when they resume.
Adjust the model. This visualizer does not read wall-clock gaps or claim that mathematical persistence is consciousness.
Paused arm: logical time does not advance during the gap. Restore the same state and feed the same inputs — it has no internal evidence that time passed.
Continued arm: dynamics evolve during the gap. Different state is possible, not guaranteed; phase can alias. An independent clock reveals the specified gap.
Select a model to inspect its prediction.
The reference is a separate trigonometric oracle. Comparing it with simulation tests our implementation, not a hypothesis of consciousness.
A quarter turn is not a fractal.
Compare complex multiplication by i with the quadratic iteration z → z² + c. Mandelbrot varies c across pixels and starts at zero; Julia fixes c and varies the starting point. Neither model tests consciousness.
Dark pixels did not escape within the selected iteration budget. Their membership is not mathematically proven.
Where periodicity changes.
The real slice x(n+1) = x(n)² + c forms different late-orbit patterns as c varies. The plotted period candidates are finite-window numerical observations, not proofs of bifurcation or chaos.
Horizontal: c from −2 to 0.35. Vertical: late orbit values. Escaped cases have no plotted tail.
How deep can a pixel go?
Explore bounded Mandelbrot and Julia zooms. We check actual neighbouring Float64 pixel coordinates before rendering; an optional sensitivity overlay compares nearby sampled viewports. Nothing here establishes chaos, life or consciousness.
Wheel: zoom at cursor · Click: centre · Drag: pan · Arrows / + / − / Home. Magenta: escape classification changed; amber: iteration count changed.