Chameleon
Accessibility Mode is ON — content will be generated in accessible format
PRODUCT · FIGURES⟵ CHAMELEON

Computed, not sketched

A figure teaches with more authority than a paragraph, which makes a wrong one worse than none. Every figure in a Chameleon tutorial is calculated on the server from the actual mathematics of the subject, then typeset like a book. This page shows how.

§1 · THE PROBLEM

A plausible diagram is a liability

Ask a language model to draw a supply-and-demand chart and it will draw something that looks right. Whether the equilibrium sits where the curves actually cross is another matter, and a student has no way to tell the difference. A diagram that is confidently wrong teaches the error more durably than text ever could, because the eye trusts a picture.

So Chameleon never lets the model draw. The model emits a small data specification, the numbers and labels taken from your material, and a deterministic renderer does the drawing.

§2 · CORRECT BY CONSTRUCTION

The math draws the picture

Each figure type computes its own domain result on the server before a single line is drawn. The Riemann rectangles are actually summed for the given function and n, and the Σ printed on the figure is that sum. The market equilibrium is solved from the curve equations. The titration curve bends at the real pKa. The circuit's currents come from Ohm's law, the Punnett ratios from the crosses, the rejection regions from the exact critical values. If the numbers in the specification are inconsistent, the figure fails closed rather than drawing something false.

riemann rectangles04xf(x)n = 8 (midpoint) · Σ ≈ 21.25
CALCULUS
Riemann sum

The rectangles sum. Σ is computed on the server for the exact function and n, so the value shown is the value.

rejection regions-202test statisticdensitycrit -1.96crit 1.96α = 0.05 (two-tailed) — shaded = reject H₀z = 2.31 → reject H₀
STATISTICS
Hypothesis test

Rejection regions drawn at the exact critical values; the test statistic lands where the math puts it.

titration curve25714titrant added (mL)pHindicator rangehalf-equivalence: pH = pKa = 4.75equivalence (pH ≈ 8.7)
CHEMISTRY
Titration curve

A weak-acid curve at its real pKa, with the equivalence point and buffer region placed by the chemistry.

punnett squareParent 1 gametesParent 2 gametesAaAaAAAaAaaa3:1 purple : white
BIOLOGY
Punnett square

Genotypes filled in and the phenotype ratio counted for you, from a monohybrid cross.

series circuitR1 = 100ΩR2 = 200ΩV = 9Vseries: R = 300Ω → I = V/R = 0.03A · drops R1: 3V · R2: 6Vsame current everywhere in a series loop; voltages divide across resistancesI
ENGINEERING
Series circuit

Ohm's law applied end to end: total resistance, current, and the voltage drop across each resistor.

payoff matrixFirm BFirm AHigh priceLow priceHigh priceLow price101021414255ringed cell = Nash equilibrium (mutual best response, underlined)
GAME THEORY
Payoff matrix

Best responses highlighted and the Nash equilibrium found on the server, shown here for the prisoner's dilemma.

REAL OUTPUT FROM THE RENDERER · UNRETOUCHED

§3 · TYPESET, NOT DECORATED

Labels measured like a book

Getting the math right is half the job; a figure also has to survive its own labels. Chameleon measures every piece of figure text with the real glyph metrics of its typeface, the same way a typesetter would, so a long axis title or a crowded legend is fitted rather than guessed at. A layout pass then resolves the whole figure: labels are kept inside the frame, stacked annotations hold their line spacing, and free-floating labels are nudged apart when they would collide. Ticks and axis titles are pinned, because a tick that moves away from its gridline is a lie.

Figures are drawn in the app's own palette tokens, so the same figure is legible on the warm paper of the light theme and the lamplight of the dark one.

§4 · THE CATALOG

47 types, nine course families

The catalog covers the figures each discipline actually leans on, and it grows by family rather than one-off. Process and relationship diagrams (flowcharts, sequence and state diagrams) render alongside them for material that is structural rather than quantitative.

ECONOMICS
supply & demand, elasticity, tax incidence, surplus shading
CALCULUS
Riemann sums, secant → tangent, slope fields, function plots
STATISTICS
hypothesis tests, regression, boxplots, histograms, Bayes frequency grids
PHYSICS
free-body diagrams, ray diagrams, vectors
CHEMISTRY
titration curves, reaction energy profiles, element ledgers
BIOLOGY
Punnett squares
ENGINEERING & CS
circuits, memory diagrams, bit grids
DECISION & GAME THEORY
payoff matrices
HISTORY & SOURCE WORK
source anatomy, parallel timelines
§5 · PREDICT, THEN REVEAL

A figure that asks first

Any figure can carry a one-line prediction prompt: commit to which way the curve shifts, or where the test statistic lands, before the answer opens. It is the cheapest form of retrieval practice there is, and it turns a figure from something you look at into something you answer to. The reader even reopens these prompts on concepts your review record marks as weak.

SERVER-COMPUTEDREAL FONT METRICSLIGHT & DARKPREDICT-THEN-REVEAL

The rule behind all of it: the model supplies the numbers from your material, and the renderer does the mathematics. Nothing on a figure is decoration.

See it on your own course.

Upload a chapter and read what comes back. Free to start, and your files stay yours.