Sawtooth Problem Visualizer

THRESHOLD (τ) ?The location of abrupt regime change. Bars with B ≤ τ fall under the "below threshold" regime (red majority); bars with B > τ fall under the "above threshold" regime (blue majority). Each tick maps to one bar on the chart.

τ = %

↙ BELOW · RED MAJORITY BLUE MAJORITY · ABOVE ↗

THRESHOLD OSCILLATION ?Automatically sweeps τ up and down between the range bounds at the chosen speed. Export one full cycle as an animated GIF or a sprite sheet (Aseprite-friendly). Width = px-per-bar × (N+1); height keeps the chart's current on-screen aspect ratio. The gap toggle controls the thin white spacer between living and dead segments. Sweep τ automatically · export the cycle

Speed 0.25 Hz Range – (τ slider units, 0–100)

Export settings: Px per bar Living/dead gap

Export cycle:

COMPOSITES ?Tie multiple primitives together with weighted rates. A composite has a single slider that drives all its member primitives at once. Each member can be negated to move in the opposite direction. Untick a composite's checkbox to disable it — its members return to their base values and their sliders are released. Tie primitives together with weighted rates.

No composites yet. Try wiring up "panic mode" (every tolerance ↓ at 100%, biases ↓ at 50%) — one slider scares the room.

MAGIC PRIMITIVE PARAMETERS Subscript = which faction the slider affects · arrow = side of threshold

BELOW THRESHOLD ↓ red majority · b ≤ 50

ABOVE THRESHOLD ↑ blue majority · b > 50

Weights how much of each triangle is active

Minority weight ?Active fraction of the minority triangle. W₁: blue minority below τ. W₂: red minority above τ.

w_b↓

w_r↑

Majority weight ?Active fraction of the majority triangle above the bias floor. W₃: red majority below τ. W₄: blue majority above τ.

w_r↓

w_b↑

Assist & bias cross-faction piggyback & constant floor

Minority assist ?Minority "piggybacks" on a fraction of the majority's bar. The minority's value becomes max(weight-derived, assist × majority). At weight=0, the assist contribution shows in full; as weight rises, the larger of the two dominates. a₁: blue minority below τ. a₂: red minority above τ.

a_b↓

a_r↑

Majority assist ?Majority "piggybacks" on a fraction of the minority's bar (rare, but useful for modeling reciprocal effects). a₃: red majority below τ piggybacks on blue minority. a₄: blue majority above τ piggybacks on red minority.

a_r↓

a_b↑

Bias ?Active fraction of the bias floor — a constant rectangle of value across all bars on its side.

β_r↓

β_b↑

Tolerance far-edge erosion of each triangle

Minority tolerance ?How much of the minority triangle is preserved. 1 = full. As tolerance ↓ toward 0, the minority is eaten away from the far edge inward. θ₁: zone 1 (blue minority below τ). θ₂: zone 2 (red minority above τ).

θ_b↓

θ_r↑

Majority tolerance ?How much of the majority faction is preserved. 1 = full. As tolerance ↓ toward 0, the majority is eaten from the far edge. θ₃: red majority below τ. θ₄: blue majority above τ.

θ_r↓

θ_b↑

SHARE ?A prefixed code that captures all primitive settings, composites, display options, oscillation, and export config. Each value carries a readable prefix (e.g. wbdn = weight·blue·below), so codes survive future parameter changes. The same code is kept live in the address bar as ?config=… — copy the URL to share, or paste a code here and click "Load from string". Also used in exported filenames. Copy the string or just the URL · paste to reproduce someone else's graph

3D TIME-SERIES ?Interpolates between saved states A and B. Drag to rotate. Scroll to zoom. Use isometric snap buttons for repeatable screenshot angles.

Frame: Blue Red Slices: 21 Smooth contours