Chameleon · visualization gallery · generated from the real renderer

Diagrams that are correct by construction.

Every figure below is the actual output of Chameleon's server-side chart system — the same SVGs its AI tutorials embed. Each preset computes its domain result before it draws: the Nash equilibrium is found, the Riemann sum is summed, the titration curve passes through the real pKa. Any chart can carry a predict-then-reveal prompt. One demo spec per registered chart type — all 47 types shown, in seven course families.

Mathematics & Calculus

Every mathematical figure computes its own result server-side — the Riemann sum really sums, the tangent slope really is the derivative.

Function plot

function-plot
Curves, intersections, marked points, shaded regions — the general-purpose graph.
two curves with intersections-1-0.170.671.52.333.174-20246810xf(x)f(x) = x²g(x) = 2x + 1

Riemann sum

riemann-sum
The rectangles really sum: Σ computed server-side for the exact expression and n.
Will the midpoint sum over- or under-estimate ∫x² here?

Midpoint balances the error on a convex curve — it lands very close (Σ ≈ 21.25 vs the true 21.33).

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

Secant → tangent

secant-tangent
Secants collapse onto the tangent as h shrinks; the limit slope is computed, not drawn.
secants collapsing to tangenta=1xf(x)h=2h=1h=0.5tangent slope ≈ 2

Taylor approximation

taylor-approx
Partial sums hug the curve order by order around the expansion point.
taylor partial sumsa=0xf(x)T1T2T3partial sums around a=0 — higher order hugs f longer

ε–δ bands

epsilon-delta
The formal limit definition made visible: a δ that actually works for the given ε.
epsilon delta bandsc=1L=1xf(x)L ± ε (ε=0.5)δ ≈ 0.22 works: inside c ± δ the curve stays in the ε-band

Slope field

slope-field
A direction field for dy/dx with traced solution curves through chosen starting points.
slope field00xydy/dx = y*(1 - y/3) — every segment shows the slope a solution must have there

Matrix transform

matrix-transform
Where î and ĵ land, the determinant, and the area factor — linear maps you can see.
linear mapî′ (2, 0)ĵ′ (1, 1)v′[ 2 1 ][ 0 1 ]det = 2area ×2

Geometry figure

geometry
Labeled points, segments with congruence ticks, circles, marked angles.
3-4-5 right triangle435ABC

Vectors

vector
Arrows with components — resultants for physics, spans for linear algebra.
two vectors with componentsab

Number line

numberline
Points, open/closed interval endpoints — inequalities and solution sets.
interval on a number line-5-4-3-2-1012345-2 < x ≤ 3-2

Economics

The classic diagrams with the equilibrium actually solved: intersections, surpluses and shifts are computed from the given curves.

Supply & demand

supply-demand
Equilibrium solved from the curves; shifts, price controls and surplus shading on demand.
supply and demand with surplusQuantityPriceDSEQ*P*

Production possibilities

ppf
Bowed-out frontier with efficient, inefficient and unattainable points placed for you.
ppf with three pointsGunsButterPPFABC

Cost curves

cost-curves
MC pierces ATC and AVC at their minima — by construction, not by sketch.
cost curve familyQuantityCost / PriceMCATCAVC

Indifference map

indifference
Curves with a budget line and the tangency point marked.
indifference curves with budget lineGood XGood YU1U2U3BudgetOptimum

AD–AS

ad-as
Aggregate demand and supply with directional shifts.
AD shift rightReal GDPPrice levelLRASADSRASAD'

Phillips curve

phillips
The inflation–unemployment trade-off, shiftable for expectations stories.
phillips curveUnemployment (%)Inflation (%)PC

Laffer curve

laffer
Revenue against tax rate with the peak marked.
laffer curveTax rate (%)RevenueRevenue-maximising ratet*

Elasticity & revenue

elasticity-revenue
Two revenue rectangles on one demand curve — where price cuts raise or lose revenue.
revenue rectanglesQuantityPriceTR1 = 32TR2 = 42Dunit elastic

Game matrix

game-matrix
Payoff matrices with best responses and the Nash equilibrium found server-side.
Where does self-interest land both firms?

Both cut prices: Low/Low is the only mutual best response.

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

Statistics & Data

ggplot-quality statistical graphics, plus the inference figures textbooks only describe: rejection regions, CLT panels, natural-frequency trees.

Histogram

histogram
Binned distribution with optional density overlay.
score distribution-0.52.55.58.511.514.5018.7837.5556.3375.193.88Exam score

Box plot

boxplot
Groups side by side, outliers flagged by the 1.5×IQR rule.
yield by treatment7.3212.1917.0621.9426.8131.68FertiliserYield (kg)ControlTreated

Regression

regression
Least-squares fit computed from the points, with the equation shown.
study hours vs score12.43.85.26.6845.0253.6662.370.9579.5988.23Study hoursScorey = 4.39x + 46.86R² = 0.97

Residual panel

residual-panel
Fit above, residuals below — how you actually judge a linear model.
fit + residualsscore vs hours — fit ŷ = 46.86 + 4.39xresiduals — a healthy fit leaves a patternless band around 0

Hypothesis test

hypothesis-test
Rejection regions at the exact critical values; the test statistic lands where it lands.
rejection regions-202test statisticdensitycrit -1.96crit 1.96α = 0.05 (two-tailed) — shaded = reject H₀z = 2.31 → reject H₀

Sampling distribution

sampling-distribution
Population vs the distribution of the mean — the CLT with SE computed.
clt panelμ=100valuedensitypopulation (σ=15)means of samples of n=25SE = σ/√n = 3 — averaging squeezes the spread

CI forest

ci-forest
Repeated confidence intervals against the true value — what 95% actually means.
repeated confidence intervals50parametersampletrue value4 samples · 1 misses the true value

Bayes as frequencies

bayes-frequency
Base-rate reasoning as a natural-frequency tree: the PPV falls out of the counts.
natural frequencies1000 people10001%have the disease10do not990test +test −test +test −true positive9false negative1false positive89true negative901A positive test means the disease: 9 of 98 positives = 9.18%count people, not probabilities — the base rate does the work

Data chart

data-chart
Plain line/scatter/bar for whatever the source tabulates.
cases per week11.82.63.44.255.0413.6222.2130.7939.3847.96WeekCasesRegion ARegion B

Physics & Engineering

Free-body diagrams that sum their forces, lenses that solve the lens equation, circuits that apply Ohm's law.

Free-body diagram

free-body
Forces drawn to scale with the resultant computed (or equilibrium detected).
free bodyW (9.8)N (9.8)F (4)ΣF (4)net force 4 — the body accelerates along ΣF

Ray diagram

ray-diagram
The three principal rays with image distance and magnification solved.
lens raysconverging lensFFobjectimageimage: real, inverted · dᵢ = 6 · m = -2

Circuit

circuit
Series circuits with current and per-resistor voltage drops from Ohm's law.
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

Wave superposition

wave-superposition
Component waves and their sum — beats emerge from close frequencies.
beats0xdisplacementwave 1 (A=1, f=3)wave 2 (A=1, f=3.5)sum — superposition adds displacements point by point

Energy ledger

energy-ledger
KE/PE bars across states with conservation checked in the caption.
energy barsEnergy (J)total = 100KEPEtopbottom

Chemistry & Biology

Reaction coordinates, titration curves at the real pKa, aufbau-filled orbitals, Punnett ratios counted for you.

Reaction coordinate

reaction-energy
Activation energy, ΔH sign, and the catalyst path overlaid.
reaction coordinatereaction coordinateEnergy (kJ/mol)with catalystreactantsproductsEa = 65ΔH = -40 (exothermic)

Titration curve

titration
Buffer region at pH = pKa, equivalence point, indicator range — computed, not traced.
titration curve25714titrant added (mL)pHindicator rangehalf-equivalence: pH = pKa = 4.75equivalence (pH ≈ 8.7)

Orbital boxes

orbital-boxes
Electron configuration filled by the aufbau principle with Hund's rule respected.
electron configuration1s↑↓2s↑↓2p↑↓↑↑O — 8 electrons: 1s² 2s² 2p⁴singly first within a subshell (Hund), opposite spins when paired (Pauli)

Punnett square

punnett
Genotypes crossed and the phenotype ratio counted.
punnett squareParent 1 gametesParent 2 gametesAaAaAAAaAaaa3:1 purple : white

Cladogram

phylo-tree
Trait acquisitions on the branches — everything to the right inherits them.
cladogramLampreyjawsSharkbony skeletonTroutHumanticks mark where a trait appears — everything to the right inherits it

Dose–response

dose-response
Sigmoid curves with EC50 pinned and the therapeutic window shaded.
sigmoid1e-91e-81e-71e-61e-550100dose (log scale)response (%)therapeutic windowagonist = 0

Law, History & Humanities

Argument structure made visual: element checklists that verdict themselves, weighed balancing tests, annotated primary sources.

Element ledger

element-ledger
A legal test's elements with met/disputed/unmet status — the verdict follows the weakest element.
element checklistAdverse possession1.Actual possession✓MET2.Open and notorious✓MET3.Hostile / without permission?DISPUTEDthe licence letter cuts against hostility4.Continuous for the statutory period✕UNMETfails: 1 element unmet — every element must be satisfied

Balancing test

balancing-scale
Weighted factors on each side; the tilt is computed from the weights.
balancingIs the measure proportionate?for (weight 2)•• Legitimate aimagainst (weight 5)••• Blanket scope•• No safeguardsagainst prevails on weight (5 vs 2)dots = assigned weight; balancing is judgment made explicit, not arithmetic

Authority pyramid

authority-pyramid
Hierarchy of norms with the level at issue highlighted.
hierarchy of normsConstitutionStatutesRegulationsCase lawthe instant casehigher authorityprevails over lower

Source anatomy

source-anatomy
A primary-source excerpt with claim/context margin notes anchored to the exact phrases.
annotated sourceZimmermann telegram, January 1917We intend to begin on the first of Februaryunrestricted submarine warfare. We shallendeavor in spite of this to keep the UnitedStates of America neutral.CLAIMthe escalation the UScould not ignoreCONTEXTsent while the US wasstill neutralread the margin first, then the text: who wrote this, for whom, and why now

Parallel timeline

parallel-timeline
Several strands against one clock — politics beside technology beside culture.
parallel lanes1914191519161917PoliticsWar beginsUS entersTechnologyPoison gasTanksone clock, several strands — read vertically to see what happened at the same time

Venn diagram

venn
Two or three sets with any region shadeable.
overlapping doctrinesCriminalCivil

Computer Science

Pointers as addresses, bits as boxes — the two diagrams every CS1 student needs, generated from real values.

Memory diagram

memory-diagram
Stack frames and heap objects with pointer arrows — a linked list you can trace.
stack and heapSTACKHEAPmain()n = 3list = •Nodeval: 7next: •Nodeval: 9variables live in frames; objects live on the heap; a pointer is just an address

Bit grid

bit-grid
Bitwise operations cell by cell with the result computed.
bit mask76543210x = 10501101001mask = 1500001111x AND mask = 900001001bit positions run 7 → 0; each step left doubles the value