Math
Logic gates
Operate Boolean gates, half and full adders, a four-bit carry chain and an edge-triggered memory bit.
Available for Windows
Makarov Math Suite
160 interactive modules bring geometry, topology, fractals, calculus, algebra, probability and algorithms into view. Rotate a surface, change a construction or follow an algorithm one step at a time.
160 modules · Page 8 / 8
Math
Finite automata and regular expressions
Compile small regular expressions into finite automata and trace word recognition through actual subset-construction transitions.
Math
Backtracking: queens and sudoku
Follow recursive backtracking for N queens and full 9×9 Sudoku, compare pruning and variable ordering, and enumerate queen solutions.
Math
Edit distance and diff
Build edit-distance tables from your own strings and trace an optimal alignment with adjustable substitution cost.
Math
String search: KMP, Boyer–Moore, Rabin–Karp
Compare naive, KMP, full Boyer–Moore and rolling-hash substring search, with recorded comparisons, prefix tables and overlapping matches.
Math
Mazes: generate and solve
Generate mazes with depth-first carving, Prim and Wilson, then compare breadth-first, A* and wall-following routes.
Math
Quadtree: space that indexes itself
Inspect adaptive quadtree partitions, nearest-neighbour pruning and collision candidates in static or moving point clouds.
Math
Fourier in two dimensions: inside JPEG
Decompose images into orthonormal 8×8 cosine blocks, remove or quantize coefficients and measure reconstruction error.
Math
Convolution: kernels on a picture
Edit 3×3 image-convolution kernels, inspect individual neighbourhood sums and compare blur, sharpening, edges and embossing.
Math
Least squares and overfitting
Fit noisy data with polynomials, move an outlier, compare training and reference errors and control overfitting with ridge regularization.
Math
k-means clustering
Step through k-means assignments and centroid updates, move centres manually and compare cluster counts on an elbow curve.
Math
Gaussian elimination: planes meeting at a point
Step through Gaussian elimination and its changing equation planes, edit a 3×3 system and examine pivoting and rank.
Math
Four colours for any map
Colour generated planar maps, inspect their adjacency graphs and compare greedy choices with a constrained backtracking search.
Math
Langton's ant
Run Langton’s ant on a sparse unbounded lattice, change multicolour turn rules and inspect the classic 104-step highway.
Math
The secretary problem: stop at 37 %
Play an optimal-stopping game with hidden candidate quality, then compare cutoff strategies with exact probabilities and Monte Carlo trials.
Math
Buffon's needle
Estimate π by throwing random needles across parallel lines, compare sample sizes and track a statistical uncertainty interval.
Math
Benford's law
Explore leading-digit distributions, multiplicative scale and counterexamples to Benford’s law using generated or pasted data.
Math
Simpson's paradox
Construct Simpson’s paradox with editable group weights and success rates, and compare subgroup and aggregate results.
Math
Counting necklaces: Burnside's lemma
Count necklaces and bracelets with Burnside’s lemma, inspect symmetry operations and verify the result by enumerating representatives.
Math
Euler's identity in motion
Connect the unit circle, sine and cosine with the vector sum of the complex exponential series and Euler’s identity.
Some modules belong to more than one Suite. Shared experiments have one description here.