EntCSFree, interactive, no sign-up
Explore. Visualise. Understand.
Algorithms, discrete maths, the theory of computation and the maths behind machine learning, each explained in plain language and paired with a visualiser you control: change the input, play it, rewind it, and watch the pseudocode follow along.
Start here
Three good places to begin.
- Algorithms
Sorting algorithms
Seven sorts on the same input, with comparison, swap and write counts side by side.
Try it: Sorting visualiser with seven algorithms and a comparison table - Tools
Graph traversal visualiser
Draw a graph, then animate BFS, DFS and Dijkstra with the frontier shown.
Try it: Drawable graph with BFS, DFS and Dijkstra animation - ML maths
Attention mechanism
Q, K and V for three tokens, a live score heatmap, and the weighted sum of values.
Try it: Three-token attention calculator with a score heatmap
Algorithms
All algorithms pages →Each page pairs a careful written explanation with a visualiser you can drive yourself: change the input, step forwards and backwards, and watch the pseudocode follow along.
- Explainer
Big-O notation
Count the steps in real loops, then compare n, n log n, n² and 2ⁿ on a live chart.
Try it: Growth-curve chart and a step counter for five loop shapes - Explainer
Recursion
Watch frames push and pop on the call stack for factorial and Fibonacci.
Try it: Call-stack stepper for factorial, Fibonacci and memoised Fibonacci - Explainer
BFS vs DFS
A queue against a stack: draw a graph and see which order each search visits it in.
Try it: Graph-traversal visualiser (BFS and DFS on a drawable graph) - Explainer
Sorting algorithms
Seven sorts on the same input, with comparison, swap and write counts side by side.
Try it: Sorting visualiser with seven algorithms and a comparison table - Explainer
Binary search
Halve the range, probe the middle, repeat: with lo, mid and hi drawn on the array.
Try it: Binary-search stepper with classic and lower-bound variants - Explainer
Dijkstra’s algorithm
Shortest paths with a priority queue: a worked table, a proof, and a graph you can redraw.
Try it: Step-through Dijkstra on a drawable weighted graph - Explainer
Hash functions
Keys in, buckets out: hash a word four ways, then watch chaining and probing handle collisions.
Try it: Hash playground, collision calculator and hash-table lab
Discrete maths
All discrete maths pages →The mathematical toolkit behind algorithms and logic. Every topic has worked examples you can check by hand, then an interactive version that computes the same thing.
- Explainer
Sets, relations and functions
Shade any set expression on a Venn diagram and test a relation for its properties.
Try it: Venn-diagram expression shader and relation-property checker - Explainer
Proof by induction
Four worked proofs revealed one step at a time, and a broken one to diagnose.
Try it: Step-reveal proofs and a numerical claim checker - Explainer
Combinatorics
An exact nPr and nCr calculator, and a Pascal’s triangle that shows its own addition rule.
Try it: nPr / nCr calculator with enumeration, and Pascal’s triangle - Explainer
Boolean algebra
The laws, De Morgan, and normal forms, with a truth-table generator built in.
Try it: Truth-table generator with CNF, DNF and equivalence checking - Explainer
Pigeonhole principle
n pigeons, k holes: why some hole gets ⌈n/k⌉, and the surprising things that follows from it.
Try it: Pigeon-dropping simulator and monotone-subsequence finder
Theory
All theory pages →What can a machine compute, and what does a program mean? Start with finite automata you can build and test, turn regular expressions into machines, see why no program can decide halting, then move on to domain theory.
- Explainer
Finite-state machines
Build a DFA in a table, see it drawn, and run strings through it one symbol at a time.
Try it: DFA builder and step-by-step string tester - Explainer
Domain theory
Why recursion needs least fixed points, and how CPOs, Scott continuity and powerdomains supply them.
Try it: Fixed-point iteration stepper (Kleene chain for factorial) - Explainer
Regular expressions to automata
Regex to NFA to DFA to minimal DFA, worked through on one example with every set shown.
Try it: Regex-to-NFA builder and subset-construction stepper - Explainer
The halting problem
Why no program can tell whether every program halts, with the paradox program played out.
Try it: Diagonal table and a “build a halting decider” challenge
ML maths
All ml maths pages →Four ideas that most of modern machine learning rests on. Each page shows the formula, works a small example you can check with a calculator, and then lets you change the numbers.
- Explainer
Gradient descent
Drag the starting point, set the learning rate, and watch it converge or blow up.
Try it: Draggable loss curve with learning-rate and step controls - Explainer
Vectors and embeddings
Bend the plane with a 2×2 matrix and measure how close toy word vectors are.
Try it: 2D matrix-transform playground and cosine-similarity explorer - Explainer
Softmax and cross-entropy
Edit the logits and watch the probabilities, the loss and the gradient update live.
Try it: Editable logits with live probabilities, loss and gradient - Explainer
Attention mechanism
Q, K and V for three tokens, a live score heatmap, and the weighted sum of values.
Try it: Three-token attention calculator with a score heatmap
Tools
All tools pages →Small, fast tools that run entirely in your browser. Nothing you type is sent anywhere, and there is nothing to sign up for.
- Tool
Truth table generator
Expression in, truth table out: with DNF, CNF, a minimal form and LaTeX.
Try it: Boolean-expression parser and truth-table generator - Tool
Graph traversal visualiser
Draw a graph, then animate BFS, DFS and Dijkstra with the frontier shown.
Try it: Drawable graph with BFS, DFS and Dijkstra animation - Tool
Recursion tree visualiser
Paste a recursive function or a recurrence and see its call tree and call count.
Try it: Call-tree drawer for JavaScript functions and recurrences - Tool
Boolean algebra calculator
A Boolean expression simplifier that names the law used at every step.
Try it: Step-by-step Boolean expression simplifier - Tool
K-map solver
Fill in a Karnaugh map and see the groups, the minimal SOP and POS, and the essential terms.
Try it: Clickable Karnaugh map with don’t-cares and drawn groups - Tool
Logic gate simulator
Wire up gates, flip the switches, and get the truth table and expression of your circuit.
Try it: Drag-and-drop circuit builder with live signals and a truth table - Tool
Regex to NFA converter
Type a regular expression and watch Thompson’s construction build its NFA, fragment by fragment.
Try it: Thompson-construction stepper and NFA string tester - Tool
NFA to DFA converter
Enter an NFA or a regex and step through the subset construction, then minimise the DFA.
Try it: Subset-construction stepper with ε-closures and DFA minimisation - Tool
DFA simulator
Edit a DFA, run strings through it step by step, batch-test them and share the machine as a link.
Try it: DFA editor, step-by-step simulator and batch tester - Tool
Sorting algorithm visualizer
Up to seven sorts race on the same data, then step through any one of them line by line.
Try it: Sorting race (8–100 values) and a step-through visualiser - Tool
LaTeX table generator
Type or paste a table, merge cells, pick booktabs, and copy clean tabular code.
Try it: Grid editor with live LaTeX output and preview - Tool
Combination calculator
Exact nCr with the cancelling shown, combinations with repetition, and a full list for small n.
Try it: nCr calculator with working, odds and enumeration - Tool
Permutation calculator
nPr, nʳ, anagrams like MISSISSIPPI and round-table seatings, with exact working.
Try it: nPr calculator with four modes and a list of arrangements
LaTeX
All latex pages →A small corner for paper writing: formatting rules that most theory venues share, what changes at the camera-ready stage, and a template we wrote ourselves.
- Guide
Formatting a CS paper in LaTeX
Page limits, \documentclass, front matter, theorem environments and the bibliography.
Try it: Pre-submission checklist you can tick off - Guide
Camera-ready checklist
Fonts embedded, PDF/A, copyright form, source bundle, and why final versions get rejected.
Try it: Camera-ready checklist with progress saved in your browser - Guide
LaTeX templates
Where the official classes live, plus a minimal article template you can copy.
Try it: Template builder: pick options and copy the generated preamble
Why visualisers?
Most of computer science happens in steps too small and too fast to see. Reading that quicksort “partitions around a pivot” is not the same as watching the pivot settle into place while the comparison counter climbs, and then trying the input that makes it slow. Every visualiser on this site computes the whole run in advance, so you can step backwards as easily as forwards, and every one is paired with a written explanation, worked examples you can check by hand, and references to the original sources.
There are 36 pages so far, and everything runs in your browser. Read more about the site.