Figure sources
Every figure in the AI chapters is an original plot generated for these notes on 24 September 2026 with NumPy, SciPy, Matplotlib, and NetworkX; no external artwork or course slides are reproduced. Each chapter’s figures come from one script in Sources/Figure code, which is the complete record of the construction. The shared module aifig.py sets the palette, fonts, and export (opaque white background, 200 dpi PNG). The tables below summarize the problems, seeds, and settings of each figure; the computing setup gives the environment and commands.
Seeds refer to numpy.random.default_rng (“NumPy seed”) or Python’s random.Random (“Python seed”). Every script accepts figure numbers as command-line arguments (for example python ch11_temporal.py 2), numbered in the order of the figures in the script, and regenerates all its figures without arguments. According to their docstrings, ch03_csp.py takes about two and three minutes for its two figures, ch04_games.py about three minutes for figure 2, ch05_sat.py a few minutes for each figure, ch07_planning.py about ten minutes, and ch10_approximate.py about two and three minutes; the others take seconds. Results from random problems are averages over the stated number of instances; they illustrate the claims in the notes and are not benchmarks.
1. Agents and uninformed search {#1-agents-and-uninformed-search}
Script: ch01_search.py.
| Local figure | Data and construction |
|---|---|
| ai-search-grid.png | A \(21\times33\) 4-connected grid with border walls, two vertical walls with gaps, and two horizontal walls; a “swamp” block (rows 4–16, columns 24–29) where entering a cell costs 6 instead of 1. Start \((10,3)\), goal \((10,29)\). Breadth-first graph search, depth-first graph search trying right, down, left, up, and uniform-cost search with a binary heap and lazy deletion; cells shaded by expansion order (viridis colormap, lightened), path in red. |
| ai-search-8puzzle.png | Left: breadth-first search backward from the 8-puzzle goal \((1,\dots,8,\text{blank})\) over all 181,440 reachable states, counted by distance. Right: five random states at each even distance from 4 to 20 (NumPy seed 0); breadth-first graph search with the goal test on generation (nodes generated and largest frontier) and iterative deepening that avoids undoing the previous move (nodes generated). |
2. Heuristic search {#2-heuristic-search}
Script: ch02_heuristic.py.
| Local figure | Data and construction |
|---|---|
| ai-heuristic-grid.png | A \(25\times41\) grid with unit costs, a cup-shaped wall open toward the start, and a short wall near the start; start \((12,4)\), goal \((12,36)\). Best-first graph search with \(f=g\), \(f=h\), \(f=g+h\), and \(f=g+2h\) for the Manhattan distance \(h\), ties broken toward larger \(g\) and then first in, first out. |
| ai-heuristic-8puzzle.png | Left: A* graph search on ten random 8-puzzle states at each even true distance from 4 to 30 (NumPy seed 0), with \(h=0\), misplaced tiles, Manhattan distance, and an additive pattern database of tiles \(\{1,2,3,4\}\) and \(\{5,6,7,8\}\) built by 0–1 breadth-first search that counts only pattern-tile moves. Right: the mean of each heuristic over all 181,440 reachable states at each true distance. |
3. Constraint satisfaction and local search {#3-constraint-satisfaction-and-local-search}
Script: ch03_csp.py.
| Local figure | Data and construction |
|---|---|
| ai-csp-queens.png | Left: \(n\)-queens for \(n=4,\dots,40\) with columns as variables and rows tried in increasing order: chronological backtracking, backtracking with forward checking, and forward checking with MRV (ties to the lowest column); assignments counted up to a budget of two million. Right: min-conflicts with \(O(n)\) conflict counters, median over five runs (NumPy seed 0) for \(n\) from 10 to 1,000 with a random initial assignment and from 10 to 10,000 with a greedy one (each queen on a least-conflicted row, ties at random). |
| ai-csp-phase.png | 40 random graphs with 100 vertices and \(m=\mathrm{round}(cn/2)\) distinct random edges for each mean degree \(c\) from 2 to 8 in steps of 0.25 (NumPy seed 1); 3-coloring by backtracking with forward checking and MRV, ties broken by the number of uncolored neighbors. Median and 90th percentile of assignments, and the fraction colorable; the dotted line marks 4.69. |
4. Adversarial search and games {#4-adversarial-search-and-games}
Script: ch04_games.py.
| Local figure | Data and construction |
|---|---|
| ai-games-alphabeta.png | Uniform trees with branching factor 5 and depths 1–9, leaf values independent uniform on \([0,1]\) (NumPy seed 0); ten trees per depth for alpha–beta with children in index order, and the first of them with children sorted best-first by their exact minimax values, which the script checks against the Knuth–Moore count. |
| ai-games-mcts.png | Tic-tac-toe; UCT with \(C=1.4\), random playouts, and rewards 1, 0.5, 0 against a player that picks uniformly among minimax-optimal moves; 100 games for each budget from 3 to 3,000 iterations per move and each side (Python seed 0); the move with the most visits is played. |
5. Propositional logic and satisfiability {#5-propositional-logic-and-satisfiability}
Script: ch05_sat.py.
| Local figure | Data and construction |
|---|---|
| ai-sat-phase.png | Random 3-SAT with three distinct variables per clause and random signs; 40 formulas for each \(n\in\{50,75,100\}\) and each ratio from 2 to 7 in steps of 0.25 (NumPy seed 0). DPLL with unit propagation, branching on the literal most frequent in the shortest open clauses; fraction satisfiable and median number of branching decisions. |
| ai-sat-growth.png | The same DPLL on 30 random formulas for each \(n\) from 20 to 140 in steps of 20 at ratios 3, 4.27, and 6 (NumPy seed 1); median decisions. The printed rate is a least-squares fit of \(\log_2\) decisions for \(n\ge60\) at the threshold. |
6. First-order logic and knowledge representation {#6-first-order-logic-and-knowledge-representation}
Script: ch06_logic.py.
| Local figure | Data and construction |
|---|---|
| ai-fol-datalog.png | Left: the ten parent facts of the chapter’s kinship example, drawn by generation, with the derived cousin pairs as dashed arcs. Right: the recursive ancestor rule on a chain of \(n\) parent facts for \(n=10,\dots,320\); rule firings of naive evaluation (all rules on all facts every round) and semi-naive evaluation (at least one fact new in the previous round), with reference curves \(n^3/3\) and \(n^2/2\). |
7. Automated planning {#7-automated-planning}
Script: ch07_planning.py.
| Local figure | Data and construction |
|---|---|
| ai-plan-heuristics.png | Blocks world with move actions between blocks and to and from the table. Ten tasks for each number of blocks from 3 to 14 (NumPy seed 0): random initial towers (each block ends a tower with probability 0.35) and a goal of all “on” atoms of another random configuration, resampled until it does not already hold. Breadth-first search (up to 7 blocks), A* with \(h^{\max}\) (up to 6), A* with \(h^{\mathrm{add}}\) (up to 10), and greedy best-first search with \(h^{\mathrm{FF}}\) (up to 14), all as graph search with unit costs; relaxation costs are computed by fixed-point iteration over the ground actions. Right: plan length divided by the breadth-first optimum. |
8. Bayesian networks and Markov networks {#8-bayesian-networks-and-markov-networks}
Script: ch08_bayesnets.py.
| Local figure | Data and construction |
|---|---|
| ai-bn-structures.png | Diagrams of the chain, fork, and collider with the middle node unobserved and observed (shaded). |
| ai-bn-explaining-away.png | Left: exact posteriors of burglary and earthquake in the burglary network (CPTs as in the chapter) by enumeration, for five evidence sets. Right: 2,000 pairs of independent standard normal “talent” and “looks” (NumPy seed 0), selected when their sum exceeds 1.5; correlations in the whole sample, the selected, and the unselected. |
9. Exact inference {#9-exact-inference}
Script: ch09_inference.py.
| Local figure | Data and construction |
|---|---|
| ai-inference-width.png | Left: induced width of elimination orders on \(n\times n\) grids (\(n=2,\dots,15\), NetworkX grid_2d_graph): row by row, min-degree and min-fill (ties by node name), and random (mean of five, NumPy seed 0). Right: five random Bayesian networks for each size from 10 to 320 nodes, each node with 0–3 parents chosen uniformly among earlier nodes, moralized and eliminated in min-fill order; median of \(\sum2^{|\text{factor}|}\) over the product factors created, for binary variables, against \(n2^n\). |
10. Approximate inference {#10-approximate-inference}
Script: ch10_approximate.py.
| Local figure | Data and construction |
|---|---|
| ai-approx-sampling.png | \(P(B\mid j,m)\) in the burglary network (exact value 0.284171835). Rejection sampling and likelihood weighting with 100 runs, and Gibbs sampling over \((B,E,A)\) with a burn-in of 100 sweeps and 20 runs, for each sample size from 100 to 100,000 (30,000 for Gibbs) (NumPy seed 0); mean absolute error, counting 0.284 when rejection keeps no sample. |
| ai-approx-ising.png | Left: five \(4\times4\) Ising models per coupling \(J\) with fields \(h_i\sim\mathcal N(0,0.3^2)\) (NumPy seed 1); exact marginals by enumeration of 65,536 states; mean field by 500 coordinate sweeps; loopy belief propagation with damping 0.5 until the messages change by less than \(10^{-10}\) or 500 iterations; Gibbs sampling with 200 burn-in and 2,000 recorded sweeps. Right: Gibbs sampling on a \(24\times24\) grid without field, started with all spins up, random-order sweeps, \(J=0.3\) and \(J=0.6\), 1,500 sweeps. |
11. Temporal probabilistic models {#11-temporal-probabilistic-models}
Script: ch11_temporal.py.
| Local figure | Data and construction |
|---|---|
| ai-temporal-casino.png | 300 rolls of the occasionally dishonest casino (switch probabilities 0.05 and 0.1; loaded die shows six with probability 0.5; NumPy seed 4), started from the stationary distribution \((2/3,1/3)\). Normalized forward and backward messages, smoothed posteriors, and Viterbi in log space with the true parameters. |
| ai-temporal-tracking.png | A constant-velocity model in two dimensions with \(\Delta t=1\), random accelerations with variance 0.1 per coordinate, position noise with variance 1, initial state \((0,0,1,0.3)\), 60 steps (NumPy seed 0). Kalman filter with initial covariance \(I\); bootstrap particle filter with multinomial resampling every step, particles initialized around the true initial state with unit noise. Left: one track, drawn with the second coordinate horizontal, and Kalman two-standard-deviation ellipses every eight steps. Right: position RMSE averaged over 30 tracks for 10 to 3,000 particles. |
12. Decision theory and the value of information {#12-decision-theory-and-the-value-of-information}
Script: ch12_decisions.py.
| Local figure | Data and construction |
|---|---|
| ai-decision-utility.png | Left: \(U(w)=\log w\) and the lottery \([0.5,20;\,0.5,180]\) in thousands. Right: \(k\) alternatives with true values \(\mathcal N(0,1)\) and estimates with added \(\mathcal N(0,\sigma^2)\) noise, \(\sigma\in\{0.5,1,2\}\); 20,000 trials per point (NumPy seed 0); mean of estimate minus true value for the alternative with the highest estimate. |
| ai-decision-vpi.png | A treat-or-wait decision with utilities 0.9 (treat, either state), 0.2 (wait, disease), 1.0 (wait, healthy); expected utilities and the value of perfect information for priors on a grid of 999 points, and the value of tests with (sensitivity, specificity) of (1, 1), (0.95, 0.9), (0.8, 0.7), and (0.6, 0.55). |
13. Causal inference {#13-causal-inference}
Script: ch13_causal.py.
| Local figure | Data and construction |
|---|---|
| ai-causal-simpson.png | Left: success counts from Charig et al. (1986) as reproduced in the causal-inference literature: A 81/87 and 192/263, B 234/270 and 55/80. Right: 500 datasets of 2,000 units (NumPy seed 0) with \(Z\sim\mathcal N(0,1)\), \(P(X=1\mid Z)=\sigma(1.5Z)\), \(Y=X+2Z+\varepsilon\), and a collider \(C=X+Y+\varepsilon'\); difference of means, least-squares adjustment for \(Z\), inverse propensity weighting with a logistic propensity fitted by 25 Newton steps, and least-squares adjustment for \(Z\) and \(C\). |
| ai-causal-iv.png | \(X=aZ+\gamma U+\varepsilon_X\), \(Y=X+\gamma U+\varepsilon_Y\) with independent standard normal \(Z\), \(U\), and noises; 1,000 units and 400 repetitions per setting (NumPy seed 1). Left: \(a=0.8\) and \(\gamma\) from 0 to 2, least-squares slope versus the Wald estimate \(\widehat{\mathrm{Cov}}(Z,Y)/\widehat{\mathrm{Cov}}(Z,X)\). Right: \(\gamma=1\) and \(a\) from 0.03 to 0.8; median and 10th–90th percentiles of the Wald estimate. |
14. Learning graphical models {#14-learning-graphical-models}
Script: ch14_learning.py.
| Local figure | Data and construction |
|---|---|
| ai-learn-trees.png | Random trees over 20 variables with 4 values (each node’s parent uniform among earlier nodes); CPT rows drawn from a Dirichlet with concentration 1 plus \(4s\) on the parent’s value, \(s=0.4\) (left) or \(s=2\) (right) (NumPy seed 0). Left: Chow–Liu with plug-in mutual information and NetworkX’s maximum spanning tree, 20 models per sample size. Right: one model, 20,000 test samples, CPTs estimated from 20 training sets per size with Dirichlet pseudocounts 0.1, 1, and 10; the fraction of test samples given probability zero by maximum likelihood is printed. |
15. Game theory and multiagent systems {#15-game-theory-and-multiagent-systems}
Script: ch15_gametheory.py.
| Local figure | Data and construction |
|---|---|
| ai-gt-regret.png | Left: Hedge self-play on rock-paper-scissors with step 0.1 for 3,000 rounds, the row player’s initial weights \((1,0,0)\). Right: ten random \(10\times10\) zero-sum games with standard normal payoffs (NumPy seed 0), Hedge self-play with step \(2\sqrt{8\ln10/10^4}\) for 10,000 rounds; duality gap of the running averages at 25 logarithmically spaced times; game values from SciPy’s linprog. |