Visualization Gallery

All 1021 animated visualizations, grouped by topic. Prefer a plain list? See the text index.

Algorithms & Data Structures

Basics 13

• Basics Mind Map
• Big-O Growth Race
• Stack: Array Implementation
• Stack: Linked List Implementation
• Queues: Array Implementation
• Queues: Linked List Implementation
• Dynamic Array: Double When Full
• Linked List: Singly and Doubly Linked
• Disjoint Sets
• Big-O, Omega, Theta
• Array vs Linked List
• Deque: Double-Ended Queue
• Infix to Postfix

Recursion 13

• Recursion Mind Map
• Factorial
• Reversing a String
• Towers of Hanoi
• N-Queens Problem
• Permutations / Combinations / Subsets
• Tail Calls and Tail-Call Optimization
• The Recursion Tree and the Master Theorem
• Recursion to an Explicit Stack
• Flood Fill
• Sudoku Solver: Backtracking
• Karatsuba Multiplication
• Closest Pair of Points

Indexing 41

• Indexing Mind Map
• Linear, Binary and Interpolation Search
• Binary Search Trees
• AVL Trees
• Red-Black Trees
• AVL vs Red-Black Tree
• Splay Trees
• Skip List
• Open Hash Tables
• Closed Hash Tables
• Closed Hash Tables, using buckets
• Separate Chaining vs Linear Probing, side by side
• Extendible Hashing
• Bloom Filter
• HyperLogLog
• LRU Cache
• Cache Eviction: LRU vs LFU vs FIFO vs CLOCK vs OPT
• Trie
• Radix Tree
• Trie vs Hash Map
• Ternary Search Tree
• B Trees
• B+ Trees
• B-Tree vs B+Tree
• Quadtree vs Geohash: Restaurants Near Me
• KD-Tree vs R-Tree: Spatial Indexing
• Fenwick Tree / Binary Indexed Tree
• Segment Tree
• Reservoir Sampling
• Count-Min Sketch
• Segment Tree vs Fenwick Tree, side by side
• Cuckoo Hashing
• Robin Hood Hashing and Swiss Tables
• Treap
• Interval Tree
• Persistent Trees: Path Copying and Structural Sharing
• 2-3-4 Tree as a Red-Black Tree
• Order-Statistic Tree
• Linear Hashing
• Sparse Table, range minimum in O
• MinHash and LSH

Sorting 18

• Sorting Mind Map
• Comparison Sorting
• Quick Sort vs Merge Sort
• Heap Sort vs Quick Sort
• Quickselect: the k-th Smallest Element
• Lomuto vs Hoare Partition
• Sorting Race
• Insertion vs Selection vs Bubble Sort
• Bucket Sort
• Counting Sort
• Radix Sort
• Comparison Sort Lower Bound
• Heap Sort
• TimSort
• Sorting Networks: Bitonic Sort and Odd-Even Merge Sort
• Three-Way Quicksort
• Bottom-up Merge Sort
• Median of Medians: Linear-Time Selection

Heap-like Data Structures 14

• Heap-like Data Structures Mind Map
• Heaps
• Priority Queues
• K-way Merge with a Heap
• Binomial Queues
• Fibonacci Heaps
• Binary vs Fibonacci Heap
• Leftist Heaps
• Skew Heaps
• Pairing Heaps
• d-ary Heap vs Binary Heap
• Running Median with Two Heaps
• Top-k with a Size-k Heap
• Indexed Heap, decrease-key in place

Graph Algorithms 38

• Graph Algorithms Mind Map
• Adjacency Matrix vs Adjacency List
• Breadth-First Search
• Depth-First Search
• BFS vs DFS
• Connected Components
• Strongly Connected Components
• Kosaraju vs Tarjan
• Bridges and Articulation Points
• Euler Path and Circuit
• Dijkstra's Shortest Path
• Bellman-Ford Shortest Path
• A* Search
• Dijkstra vs A*
• Dijkstra vs Bellman-Ford
• Floyd-Warshall vs Johnson
• Floyd-Warshall
• Prim's Minimum Cost Spanning Tree
• Kruskal Minimum Cost Spanning Tree Algorithm
• Prim vs Kruskal
• Topological Sort
• Topological Sort
• Graph Coloring
• P vs NP: Checking vs Finding
• Maximum Flow
• Grid Pathfinding
• Grid Pathfinding Side by Side
• Grid Replanning: A* from Scratch vs D* Lite
• Any-Angle Path Planning: A* vs Theta*
• Maze Generation Side by Side
• Lowest Common Ancestor: Binary Lifting
• Bipartite Matching and the Hungarian Algorithm
• Stable Matching: the Gale-Shapley Algorithm
• Shortest Paths in a DAG, relax edges in topological order
• Dinic's Max Flow
• 0-1 BFS
• PageRank
• Louvain Community Detection

Dynamic Programming 32

• Dynamic Programming Mind Map
• Calculating nth Fibonacci number
• Making Change
• Longest Common Subsequence
• 0/1 Knapsack
• Coin Change
• Greedy vs DP Coin Change
• Plain Recursion vs Memoization vs Tabulation
• Top-Down vs Bottom-Up DP, side by side
• Edit Distance
• Matrix Chain Multiplication
• Longest Increasing Subsequence
• House Robber and Climbing Stairs
• DP on Trees: Maximum Weight Independent Set
• Weighted Interval Scheduling
• Kadane's Algorithm: Maximum Subarray Sum
• Grid Paths: Unique Paths and Minimum Path Sum
• Subset Sum and Equal Partition
• Rod Cutting
• Maximal Square of 1s
• Word Break
• Longest Palindromic Subsequence and Substring
• Optimal Binary Search Tree
• CYK Parsing
• Needleman–Wunsch vs Smith–Waterman
• Wildcard and Regex Matching DP
• Egg Dropping Puzzle
• Held–Karp Travelling Salesman DP
• Longest Path in a DAG, DP as a path over subproblems
• Stock Trading State Machine DP
• Rolling Array Space Saving in DP
• Bitmask DP over Subsets

String & Greedy Algorithms 20

• String & Greedy Algorithms Mind Map
• Knuth-Morris-Pratt
• String Search Race
• Z-Algorithm String Matching
• Huffman Coding
• Base64 Encoding & Decoding
• Rabin-Karp Rolling Hash Search
• Interval Scheduling
• Fractional Knapsack
• Interval Partitioning
• Suffix Array
• Manacher's Algorithm, Longest Palindromic Substring
• Aho-Corasick Multi-Pattern Search
• LZ77 and DEFLATE
• Gap Buffer vs Rope vs Piece Table
• Burrows–Wheeler Transform
• Scheduling to Minimize Lateness: Earliest Deadline First
• Suffix Tree, Ukkonen's Algorithm
• LZW Compression
• Sliding Window Substrings

Geometric Algorithms 20

• Geometric Algorithms Mind Map
• 2D Rotation and Scale Matrices
• 2D Rotation and Translation Matrices
• 2D Changing Coordinate Systems
• 3D Rotation and Scale Matrices
• 3D Changing Coordinate Systems
• Fourier Series and the FFT
• Sampling and Aliasing: Nyquist and the Wagon Wheel
• Convex Hull: Graham Scan vs Gift Wrapping
• Delaunay Triangulation: Bowyer–Watson and Edge Flips
• Point in Polygon: Ray Casting vs Winding Number
• Segment Intersection: Sweep Line vs Brute Force
• Voronoi Diagram: Nearest-Site Cells
• Bézier Curves
• JPEG Compression: DCT and Quantization
• Rasterization: Edge Functions and the Z-Buffer
• Ray Tracing vs Rasterization
• Ear Clipping: Cutting a Polygon into Triangles
• Bresenham's Line Algorithm
• Phong Shading: Ambient, Diffuse, Specular

Mathematics

Number Theory 19

• Number Theory Mind Map
• Number Bases and Two's Complement
• Euclidean Algorithm
• Sieve of Eratosthenes
• The Ulam Spiral: Primes on Diagonals
• Modular Exponentiation and Toy RSA
• Fermat's Little Theorem and Euler's Theorem
• The Times-Table Circle: i → k·i mod N
• The Sunflower Spiral: Vogel's Model and the Golden Angle
• Extended Euclid, Modular Inverse and Toy RSA
• Prime Factorization
• Chinese Remainder Theorem
• The Collatz Conjecture: 3n + 1 Hailstones and the Collatz Seaweed
• Hamming Code
• Reed-Solomon Erasure Coding
• Primality Testing: Fermat and Miller–Rabin
• Linear Diophantine Equations
• How the Primes Thin Out: π
• Continued Fractions: Best Rational Approximations

Algebra & Functions 31

• Algebra & Functions Mind Map
• Function Transformations
• Function Composition and Inverses
• Linear Functions: Slope and Intercept
• Quadratic Equations
• Systems of Equations
• What a, b and c Do to a Parabola
• Polynomial Division
• Cubic Functions: What a, b, c, d Do
• Types of Asymptotes
• Rational Functions: What a, b, c, e, f Do
• Exponentials and Logarithms
• Exponential Graphs: What a, b, h, k Do
• Damped Oscillation: What A, γ, ω, φ Do
• The Heart Curve: a Sine Wave Filling a Heart
• A Wave in Any Envelope: h
• Driven Oscillator: Resonance, Phase Lag and Q
• Spring Oscillator: What m, k, A, ω, f, T Do
• Simple Pendulum: What L, g, m, θ₀ and T, f, ω Do
• Elastic and Inelastic Collisions: What m₁, m₂, v₁, v₂, e Do
• Collisions in 2-D: What m₁, m₂, v₁, b, e Do
• Ballistic Pendulum: What m, M, v, L Do
• Projectile Motion: What v₀, θ, g and h Do
• A Block on a Ramp: What θ, m, μs, μk Do
• Orbital Motion: Circles, Ellipses, Escape and Kepler's Laws
• Bernoulli's Principle: Fast Fluid, Low Pressure
• RC Circuit: Charging and Discharging a Capacitor
• Lens Ray Diagrams: Where the Image Forms
• Arithmetic vs Geometric Sequences: Add a Step or Multiply by a Ratio
• Linear Inequalities: Shade the Side That Makes It True
• Absolute Value and Piecewise Functions

Trigonometry & Geometry 35

• Trigonometry & Geometry Mind Map
• The Pythagorean Theorem
• Proofs Without Words
• Circle Theorems
• Triangle Centres
• The Law of Sines and the Law of Cosines: Solving Any Triangle
• Right-Triangle Ratios: SOH CAH TOA
• Euler's Formula V − E + F = 2
• The Unit Circle: sin, cos, tan
• Angle Addition Identities: sin
• Sine Waves: What a, b, c, d Do
• Cosine Waves: What a, b, c, d Do
• Wave Interference: Two Coherent Sources
• Standing Waves on a String: What n, L, T, μ Do
• Transverse and Longitudinal Waves: a Rope, Sound and Water
• Group Velocity and Phase Velocity: Beats, Wave Packets, Dispersion
• The Doppler Effect: Why a Passing Siren Changes Pitch
• Tangent Graphs: What a, b, c, d Do
• Polar Coordinates
• The Rose Curve r = cos kθ: Petals as k Goes from 0 to 10
• The Lemniscate of Bernoulli
• The Maurer Rose: Straight Lines Across a Rose
• Lissajous Figures: Two Sine Waves Drive One Pen
• Harmonograph: a Pen Driven by Damped Pendulums
• Spirograph: Hypotrochoids and Epitrochoids
• The Butterfly Curve: Six Laps of a Polar Pen
• The Superformula: Gielis Shapes from Four Numbers
• Ellipse: What a, b, h, k Do
• Parabola: Focus, Directrix and What p, h, k Do
• Hyperbola: What h, k, a, b Do
• Conic Sections: What A, B, C, D, E, F Do
• Conics by Eccentricity: r = ep/
• Inverse Trig Functions: Restrict the Domain, Then Flip
• Archimedes' π: Polygons Inside and Outside a Circle
• The Cycloid: a Point on a Rolling Wheel

Quadric Surfaces 25

• Quadric Surfaces Mind Map
• Quadric Surfaces
• Ellipsoid
• Hyperboloid of One Sheet
• Hyperboloid of Two Sheets
• Elliptic Paraboloid
• Hyperbolic Paraboloid
• Elliptic Cone
• Level Surfaces x² + y² − z² = k
• Elliptic Cylinder
• Hyperbolic Cylinder
• Plane Equation
• Surfaces of Revolution
• Quadric Classification
• Tangent Plane and Normal to a Quadric
• Surfaces by Degree: Planes, Quadrics, Cubics, Quartics
• Monkey Saddle
• Cubic Surface x³ + y³ + z² = 1
• Cayley's Nodal Cubic
• Quartic Surface x⁴ + y⁴ − z⁴ = 1
• Kummer Surface
• Degenerate Quadrics: Plane Pairs, a Line, a Point, or Nothing
• Where Two Quadrics Meet: Steinmetz, Viviani and the Triple Integral
• Dandelin Spheres: Why a Cone's Cut Is an Ellipse
• Parametrizing Quadric Surfaces

Linear Algebra & Complex Numbers 32

• Linear Algebra & Complex Numbers Mind Map
• 2D Vectors and the Dot Product
• Span, Linear Independence and Basis
• Determinant: how a 2×2 matrix scales area
• Gaussian Elimination
• Eigenvectors & Eigenvalues
• Complex Numbers
• Conformal Maps: Complex Functions Bend the Plane
• Matrix Multiplication
• Linear Transformations
• Rotation Matrix
• Reflection Matrix
• Scaling Matrix
• Shear Matrix
• Projection Matrix
• Squeeze Mapping
• Composing Transforms
• Affine Transforms: Translation as a 3×3 Matrix
• Inverse Matrix
• Diagonalization: A = P D P⁻¹
• Column Space and Null Space
• Gram–Schmidt and QR
• 3D Rotation Matrix
• 3D Reflection Matrix
• Projection Matrix in 3D
• 3D Shear Matrix
• Quaternions
• Perspective Projection: the Pinhole Camera
• Least Squares as Projection
• SVD and PCA in 2D
• LU Decomposition
• The Cross Product in 3D: Perpendicular, Length = Area

Calculus 44

• Calculus Mind Map
• Limits & Continuity
• Derivative as a Limit
• Local Linearity: Zoom In
• Derivative Rules as Pictures
• f, f′, f″: Reading Derivative Graphs
• Optimization Problems: the Box and the Fence
• Critical & Singular Points
• Mean Value Theorem
• Related Rates: Ladder, Balloon and Cone Tank
• Accumulation: Rate → Amount
• Riemann Sums
• Numerical Integration: Riemann vs Trapezoid vs Simpson
• Geometric Series
• Taylor Series
• Infinite Series for π: Leibniz to Ramanujan
• Polynomial Interpolation vs Splines
• Fourier Series, Harmonic by Harmonic
• Fourier Epicycles: Drawing a Shape with Spinning Circles
• The Weierstrass Function: Continuous Everywhere, Differentiable Nowhere
• Newton's Method
• Root Finding: Bisection vs Newton vs Secant
• The Chain Rule
• Fundamental Theorem of Calculus
• Integration by Parts and Substitution
• Volumes by Slicing
• Improper Integrals
• Six Types of Integrals
• Euler's Method
• Runge–Kutta vs Euler
• Phase Portraits of Linear Systems x′ = Ax
• The Heat Equation: Diffusion Step by Step
• The Logistic Map: from a Fixed Point to Chaos
• The Lorenz Attractor: Deterministic Chaos
• The Double Pendulum: Normal Modes and Chaos
• The Laplace Transform
• Level Curves and Contour Maps
• Gradients and Lagrange Multipliers: ∇f = λ∇g
• Implicit Differentiation
• L'Hôpital's Rule: 0/0? Compare the Slopes
• Series Convergence Tests: Does the Sum Settle?
• Arc Length: a Sum of Tiny Hypotenuses
• Partial Derivatives and the Tangent Plane
• Divergence and Curl: Spread vs Spin

Fractals 11

• Fractals Mind Map
• The Mandelbrot Set: z → z² + c, Zooms and Orbits
• Julia Sets of z → z² + c
• The Chaos Game: Random Jumps Draw the Sierpinski Triangle
• The Barnsley Fern: Four Affine Maps Picked at Random
• Fractal Curves: Koch Snowflake, Dragon Curve, Hilbert Curve
• Box-Counting Dimension: Halve the Boxes, Count Again
• L-Systems: String Rewriting and Turtle Graphics
• The Cantor Set and the Menger Sponge: Cut the Middle Thirds
• Newton Fractals: Which Root Does Each Start Find?
• Midpoint Displacement: Fractal Terrain by Split, Nudge, Halve

Physics & Circuits 21

• Physics & Circuits Mind Map
• RLC Circuits: Charging, Ringing and Resonance
• Ohm's Law and Kirchhoff's Laws: Solving a Resistor Network
• Diodes and Rectifiers: AC In, DC Out
• The Ideal Op-Amp: Two Rules, Four Circuits
• Faraday's Law: Electromagnetic Induction and Lenz's Law
• Electric Field Lines: Coulomb's Law and Point Charges
• A Charge in a Magnetic Field: the Lorentz Force
• Electromagnetic Waves: E, B, c and Polarization
• A Dipole Antenna: How Radio Waves Are Sent and Received
• Polarizers and Malus's Law: Linear, Circular and Unpolarized Light
• Refraction: Why Light Bends, Snell's Law and Total Internal Reflection
• Diffraction: Single Slit, Double Slit and Gratings
• The Photoelectric Effect: Light Comes in Photons
• Special Relativity: the Light Clock, Length Contraction and Spacetime
• Quantum Tunneling and the Particle in a Box
• The Transistor as a Switch: MOSFET, BJT, CMOS NOT and NAND
• The Carnot Heat Engine: Work Is the Loop's Area
• Ideal Gas and the Maxwell–Boltzmann Distribution
• The Electric Motor and Generator: a Current Loop in a Field
• The Bohr Atom and the Hydrogen Spectrum

Probability & Statistics 23

• Probability & Statistics Mind Map
• Bayes' Theorem
• Pascal's Triangle
• Permutations vs Combinations
• Expected Value and the Law of Large Numbers
• Central Limit Theorem
• Monte Carlo Estimation of π
• Normal Distribution, z-Scores and Confidence Intervals
• Mean vs Median vs Mode
• Correlation and Scatter Plots, Pearson r
• Variance and Standard Deviation
• Markov Chains and Random Walks
• Binomial vs Poisson
• Hypothesis Testing with a Coin
• Simpson's Paradox: Correlation vs Causation
• Confidence Intervals
• Frequentist vs Bayesian Inference
• The Birthday Paradox
• The Monty Hall Problem
• PDF vs CDF
• Exponential Waiting Times
• Probability Tree Diagrams
• The Chi-Square Test: Is This Die Fair?

Economics & Money 20

• Economics & Money Mind Map
• Supply and Demand: How the Price Finds Equilibrium
• Circular Flow of Money: Households, Firms, Government
• Flow of Funds: Who Lends to Whom
• Quantity Theory of Money: MV = PY
• Keynes's Liquidity Preference Theory
• The IS–LM Model: Fiscal vs Monetary Policy
• Monetary Transmission Mechanism
• The Credit Cycle: Loans, Collateral, Minsky
• Portfolio Rebalancing and Flight to Quality
• Global Dollar Liquidity and Swap Lines
• The AD–AS Model: Demand and Supply Shocks
• The Phillips Curve and Expectations
• Bank Runs: Panic, Fire Sales and Backstops
• Comparative Advantage: Why Both Countries Gain from Trade
• Present Value and Bonds
• Taylor Rule
• Exchange Rates and Parity: Rate Gaps Move the Currency
• Solow Growth Model
• Prisoner's Dilemma

Logic, Sets & Counting 14

• Logic, Sets & Counting Mind Map
• Truth Tables and Sets
• Inclusion–Exclusion and the Pigeonhole Principle
• Catalan Numbers
• The Pigeonhole Principle
• Proof by Induction as Falling Dominoes
• Regex to NFA to DFA
• Pushdown Automaton: a Stack Counts aⁿbⁿ
• Turing Machine: Tape, Head and State Table
• Karnaugh Maps
• DFA Minimization
• Quine–McCluskey Method
• SAT Solving with DPLL
• Cantor's Diagonal Argument

Systems

Databases & Storage 43

• Databases & Storage Mind Map
• B+ Tree as a Database Index
• Clustered vs Secondary Index, side by side
• LSM Tree vs B+ Tree
• Row Store vs Column Store
• Snowflake vs UUIDv4 vs UUIDv7
• How MySQL Runs a Query
• How MySQL Executes JOIN, GROUP BY and ORDER BY
• How PostgreSQL Runs a Query
• How PostgreSQL Executes JOIN, GROUP BY and ORDER BY
• How a SELECT Runs: WHERE, GROUP BY, HAVING, ORDER BY
• Relational Algebra: Tables In, Table Out
• How a Query Planner Picks a Plan
• MariaDB Rewrites a Query Tree, the Book's Query Q
• MariaDB: Merging Views and Unnesting Subqueries
• MariaDB Histograms: Where Row Estimates Come From
• MariaDB Access Paths: What a SELECT Costs
• MariaDB: How the Optimizer Picks a Join Order
• MariaDB Cost-Based Optimization: a Worked Example
• MariaDB EXPLAIN vs ANALYZE and Top-k LIMIT
• MariaDB Table Elimination and Impossible WHERE
• Nested Loop vs Hash Join vs Merge Join
• Database Connection Pool
• Connection Pool Settings in Action
• The N+1 Query Problem
• How MongoDB Runs a Command
• MongoDB Sharding: mongos, Chunks and the Balancer
• MongoDB Replica Set Elections and Rollback
• MongoDB Read Concern and Causal Consistency
• MongoDB Multi-Document Transactions
• MongoDB Aggregation Pipeline, Stage by Stage
• MongoDB Indexes: Compound, ESR, Multikey, Covered
• MVCC and Isolation Levels
• Optimistic vs Pessimistic Locking
• Two-Phase Locking and Deadlock Detection
• Write-Ahead Logging and ARIES Crash Recovery
• SQLite Internals
• Data Models: Relational vs Document vs Graph
• Database Normalization: 1NF, 2NF and 3NF
• ER Model to Tables: Keys and Foreign Keys
• Inverted Index: From Documents to Posting Lists
• SQL Window Functions: an Aggregate for Every Row
• Timestamp Ordering Concurrency Control

PostgreSQL Internals 21

• PostgreSQL Internals Mind Map
• PostgreSQL Process Architecture
• PostgreSQL Shared Buffers and the Clock Sweep
• Inside a PostgreSQL Heap Page
• How PostgreSQL Stores Big Values
• PostgreSQL Free Space Map and Visibility Map
• PostgreSQL pg_xact
• PostgreSQL XID Wraparound and Freezing
• PostgreSQL VACUUM and Autovacuum
• The PostgreSQL Lock Manager
• Serializable Snapshot Isolation in PostgreSQL
• PostgreSQL WAL Internals
• PostgreSQL Checkpoints
• PostgreSQL Streaming Replication and Hot Standby
• PostgreSQL Logical Decoding and Logical Replication
• PostgreSQL Index Types
• PostgreSQL Bitmap Index Scan and Bitmap Heap Scan
• PostgreSQL Parallel Query
• The PostgreSQL Executor Pipeline
• PostgreSQL Base Backup and Point-in-Time Recovery
• PostgreSQL Partitioning and Partition Pruning

MySQL / InnoDB Internals 22

• MySQL / InnoDB Internals Mind Map
• The InnoDB Buffer Pool: Midpoint LRU and Flushing
• Inside an InnoDB Index Page
• InnoDB Tablespace Layout: Pages, Extents and Segments
• The InnoDB Change Buffer
• InnoDB Adaptive Hash Index
• InnoDB Doublewrite Buffer and Torn Pages
• InnoDB Undo Logs, Read Views and Purge
• InnoDB Isolation: Snapshot Reads vs Current Reads
• MVCC in PostgreSQL vs InnoDB, side by side
• InnoDB Record, Gap and Next-Key Locks
• InnoDB Row Lock Structures: lock_sys Hash and Lock Bitmaps
• MySQL Metadata Locks and Online DDL
• InnoDB Redo Log Internals
• MySQL Binlog Group Commit
• InnoDB Crash Recovery
• MySQL Replication Internals
• MySQL Group Replication and InnoDB Cluster
• MySQL Index Access Paths and EXPLAIN
• InnoDB AUTO-INC Lock Modes
• Physical Hot Backup with mariadb-backup
• MariaDB Threads and Connections

Distributed Systems 80

• Distributed Systems Mind Map
• Primary–Replica Replication: Sync vs Async, Lag and Failover
• Sync vs Semi-sync vs Async Replication: Side by Side
• Consistency Patterns: Weak, Eventual, Causal, Strong
• The CAP Theorem: CP vs AP Side by Side
• How Raft Elects a Leader and Replicates a Log
• Raft vs Multi-Paxos, Side by Side
• etcd: the Store Behind Kubernetes
• Paxos: How Three Acceptors Agree on One Value
• Lamport Clocks and Vector Clocks
• Hybrid Logical Clocks and TrueTime: Ordering Writes With Skewed Clocks
• Lamport Clocks vs Vector Clocks: Detecting Concurrent Writes
• Leader Election: Bully vs Ring
• Byzantine Fault Tolerance: PBFT
• Gossip and SWIM: How a Cluster Knows Who Is Alive
• Chandy–Lamport Distributed Snapshot
• Quorum Reads and Writes
• Leader-based vs Leaderless Replication
• CRDTs: Conflict-Free Replicated Data Types
• Merkle Trees for Anti-Entropy Repair
• Partitioning vs Sharding
• Consistent Hashing
• Rendezvous vs Consistent vs Mod-N Hashing
• Range vs Hash Partitioning
• Rebalancing Partitions: Hash mod N vs Fixed vs Dynamic
• MapReduce: Word Count, Shuffle and Failures
• MapReduce Joins: Sort-Merge, Skew and Map-Side Joins
• Saga vs Two-Phase Commit
• Two-Phase Commit
• Saga: Orchestration vs Choreography
• Transactional Outbox and Inbox
• Idempotency Keys: Same Key Twice = One Charge
• Delivery Semantics: At-most-once vs At-least-once vs Exactly-once
• Event Sourcing and CQRS
• Change Data Capture: Log Tailing from the WAL to Kafka
• How Kafka Moves a Message
• Push vs Pull Messaging: RabbitMQ vs Kafka
• Log vs Queue: Kafka vs RabbitMQ, side by side
• Kafka Consumer Groups: Rebalancing, Duplicates and Exactly-Once
• Kafka Log Segments: How a Partition Is Stored on Disk
• Kafka Replication: Fetching, the ISR, Leader Epochs and Truncation
• Kafka Log Compaction
• Kafka KRaft: the Controller Quorum and the Metadata Log
• Kafka Zero Copy
• How Redis Sentinel Fails Over a Master
• How Redis Cluster Shards and Fails Over
• How Redis's Keyspace Dict Rehashes
• How a Redis Sorted Set Is Stored
• How Redis Stores Small and Large Values
• How Redis Forgets Keys: Expiry and Eviction
• How Redis Saves Data: RDB Snapshots and the AOF
• How Redis Replicas Sync: PSYNC and the Backlog
• Redis Streams and Consumer Groups
• Redis Transactions and Scripts
• Distributed Locks and Fencing Tokens
• Cache Strategies Side by Side
• Circuit Breaker and Bulkhead
• Retry, Exponential Backoff and Jitter
• Monolith vs Microservices
• Distributed Tracing with OpenTelemetry
• Rate Limiting: Token Bucket vs Leaky Bucket
• Rate Limiting with Windows: Fixed, Sliding Log, Sliding Counter
• Backpressure: When the Producer Is Faster than the Consumer
• Latency vs Throughput
• Kubernetes Cluster Architecture
• The Life of a Kubernetes Pod
• How the Kubernetes Scheduler Places a Pod
• How Kubernetes Talks to containerd and Docker
• Kubernetes Container Lifecycle Hooks
• How the Kubernetes Control Plane and Nodes Talk
• Kubernetes Autoscaling: HPA and Cluster Autoscaler
• Kubernetes Config and Secrets: Helm, GitOps, External Secrets, Spring Boot
• Bitcoin Merkle Trees and SPV Proofs
• Object Storage: How an S3-style Store Keeps a File
• Proof of Work: Mining a Chain of Blocks
• Two Generals and FLP Impossibility
• HDFS / GFS File Layout
• Chain Replication: Write at the Head, Read at the Tail
• Hedged Requests
• Service Discovery

Software Design 29

• Software Design Mind Map
• Domain Logic Patterns: Transaction Script, Table Module, Domain Model
• Data Source Patterns: Who Writes the SQL
• Inheritance Mapping: Single Table vs Class Table vs Concrete Table
• Offline Locks: Optimistic vs Pessimistic
• Remote Facade and Data Transfer Object
• The Money Pattern and Value Object
• SOLID Principles
• Hexagonal Architecture: Ports and Adapters
• MVC vs MVVM: One Click Through Each Layer
• Test Doubles: Stub, Fake and Mock
• The Observer Pattern vs Publish–Subscribe
• Virtual DOM Diffing: How React Reconciles
• Strategy and Factory Method Patterns
• Inheritance vs Composition
• Decorator, Proxy and Adapter: Wrappers That Share One Interface
• The Command Pattern: Undo and Redo
• The State Pattern
• Git Three-Way Merge
• Git Packfiles
• Git Merge vs Rebase
• Git Branches and HEAD: Pointers to Commits
• Git Reset vs Revert vs Restore: Undo Side by Side
• Git Objects: Blobs, Trees and Commits
• Builder and Singleton Patterns
• The Composite and Visitor Patterns
• Chain of Responsibility
• Coupling and Cohesion: One Change, One Module
• Git Bisect: Binary Search for the First Bad Commit

Networking 50

• Networking Mind Map
• Internet Protocol Layers
• Cyclic Redundancy Check
• How ARP Finds a MAC Address
• Subnets and CIDR: Is the Destination on My Subnet?
• How a Router Forwards a Packet
• Distance Vector vs Link State Routing
• Hub vs Switch vs Router
• Anycast and BGP: One Address, Many Sites
• How NAT Shares One Public Address
• How a WebRTC Call Gets Through NATs
• IPv4 vs IPv6
• How Docker Networking Works on One Host
• How a VPN Works: a WireGuard Tunnel
• Forward Proxy vs Reverse Proxy, Side by Side
• L4 vs L7 Load Balancing, Side by Side
• How a Device Gets an IP Address
• The Life of an HTTP Request in Kubernetes
• Kubernetes Service Types
• How a DNS Name Is Resolved
• NTP: How a Clock Sets Itself From Four Timestamps
• How a CDN and Route 53 Work
• How an API Gateway Handles a Request
• How a Service Mesh Handles a Request: Istio and Envoy
• TCP vs UDP
• The Jitter Buffer in a Voice Call
• ARQ: Stop-and-Wait vs Go-Back-N vs Selective Repeat
• How TCP Congestion Control Works
• TCP Congestion Control Compared: Reno vs CUBIC vs BBR
• How an HTTP Connection Is Established
• A TCP Socket in Linux
• The Linux Listen Backlog
• Unix Socket vs TCP on Loopback
• TCP Three-Way Handshake and the Listen Queues
• How an HTTPS Connection Is Established
• TLS Certificate Chain and Revocation
• HTTP/1.1 vs HTTP/2 vs HTTP/3
• The QUIC Handshake vs TCP + TLS 1.3
• TLS 1.2 vs TLS 1.3 Handshake
• WebSocket vs SSE vs Long Polling
• How a gRPC Call Travels over HTTP/2
• REST vs GraphQL vs gRPC
• How HTTP Caching Works: Browser Cache, CDN and Origin
• TCP Flow Control: the Receive Window
• How Traceroute Works
• VLANs: One Switch, Several Networks
• Wi-Fi CSMA/CA
• Stateful Firewall vs a Stateless ACL
• Router Queues and Bufferbloat
• Adaptive Bitrate Video Streaming

Web & Security 34

• Web & Security Mind Map
• How Browser Cookies Work
• CORS and the Preflight Request
• CSRF and SameSite Cookies
• XSS and Content-Security-Policy
• How OAuth 2.0 Works
• JWT vs Session Cookies
• HttpOnly Cookie vs localStorage
• How a Digital Signature Works
• Email Delivery with SPF, DKIM and DMARC
• How Diffie-Hellman Key Exchange Works
• Salt vs Pepper: Storing Passwords
• Symmetric vs Asymmetric Encryption
• Encryption vs Hashing
• Inside AES-128 and SHA-256
• Block Cipher Modes: ECB vs CBC vs GCM
• OWASP A02:2025 Security Misconfiguration
• OWASP A03:2025 Software Supply Chain Failures
• OWASP A04:2025 Cryptographic Failures
• OWASP A06:2025 Insecure Design
• OWASP A07:2025 Authentication Failures
• How TOTP Two-Factor Codes Work
• OWASP A08:2025 Software or Data Integrity Failures
• OWASP A09:2025 Security Logging and Alerting Failures
• OWASP A10:2025 Mishandling of Exceptional Conditions
• OWASP A01:2025 Broken Access Control
• How Kerberos Works
• Mutual TLS: Both Sides Show a Certificate
• Password Hashing: Fast vs Slow Hashes
• Server-Side Request Forgery
• Elliptic Curve Cryptography
• Timing Attacks and Constant-Time Comparison
• RBAC vs ABAC
• Path Traversal and Command Injection

Servers & Event Loops 27

• Servers & Event Loops Mind Map
• How Tomcat handles an HTTP request
• How nginx Handles an HTTP Request
• nginx Proxy Request: Memory, System Calls and Kernel
• Prefork vs Threads vs Events
• Scale Up vs Scale Out: vertical vs horizontal scaling
• Canary, Blue/Green and Rolling Deployments
• Graceful Shutdown: Stop Accepting, Drain, Then Exit
• A/B Testing
• Linux epoll
• select vs poll vs epoll, Side by Side
• How a request is handled in Tomcat and Linux epoll
• io_uring vs epoll
• Blocking vs Non-blocking vs Async I/O
• Reactor vs Proactor
• The Node.js Event Loop
• How the Browser Runs JavaScript: the Event Loop
• Debounce vs Throttle vs Raw Events
• Callbacks vs Promises vs Async/Await: One Task, Three Ways
• How the Browser Renders a Page: DOM to Pixels
• Server-side vs Client-side Rendering
• Node.js Under the Hood: libuv and Where the Work Runs
• How Redis Serves Many Connections with One Thread
• The Python asyncio Event Loop
• SO_REUSEPORT and accept: Who Gets the New Connection
• Service Worker Cache
• Serverless Cold Start

Operating Systems 56

• Operating Systems Mind Map
• How Linux Boots
• systemd Units: Dependencies, Restart and Socket Activation
• How a C Program Is Compiled, Linked, Loaded and Started
• Little-Endian vs Big-Endian
• Static vs Dynamic Linking, side by side
• How a C/C++ Program Is Compiled and Run: What C++ Adds
• How Linux Loads a Program
• A Linux System Call, Step by Step
• How Linux Delivers a Signal
• How strace and gdb Work
• TTY, PTY and Job Control: What Ctrl-C Really Does
• What a Container Really Is
• Containers vs Virtual Machines, Side by Side
• seccomp and eBPF: Programs Inside the Kernel
• How a Dockerfile Becomes Image Layers
• Linux Context Switch
• Process vs Thread, side by side
• The Interrupt-Driven I/O Cycle
• Kinds of Interrupts in Linux
• CPU Scheduling
• Linux Load Average, Explained
• Preemptive vs Cooperative scheduling
• Real-Time Scheduling and Priority Inversion
• Disk Scheduling
• Banker's Algorithm
• Deadlock Detection and Recovery
• Linux Virtual Memory
• The TLB and the x86-64 Page Walk
• Copy-on-Write fork
• A Linux Process from fork
• How the Shell Runs ls | grep foo
• IPC: Pipe vs Message Queue vs Shared Memory
• Paging and Page Replacement
• Paging vs Segmentation
• Direct Memory Access: How a NIC Moves Packets
• How Linux Receives a Packet
• How a File System Survives a Crash
• Copy-on-Write File Systems vs Journaling, btrfs / ZFS vs ext4
• The Page Cache: read vs mmap
• How a Hard Disk Reads and Writes Data
• How an SSD Reads and Writes Data
• RAID 0, 1, 5 and 10
• The Linux Block Layer: How a Write Reaches the Disk
• What open
• Hard Link vs Symbolic Link: Side by Side
• Linux Permissions: uid, rwx, setuid and Capabilities
• The Buddy Allocator
• The Slab Allocator: How Linux kmalloc Works
• Linux Out of Memory: Reclaim, kswapd and the OOM Killer
• Stack vs Heap in C
• glibc malloc vs jemalloc vs tcmalloc
• Thrashing and the working set
• Swap Out and Swap In
• Monolithic Kernel vs Microkernel
• How a Hypervisor Runs a VM

Concurrency 29

• Concurrency Mind Map
• Concurrency vs Parallelism
• Race Condition: count++ and the Lost Update
• Bounded Buffer / Producer–Consumer
• Monitor & Condition Variables
• Readers–Writers Problem
• Dining Philosophers
• Deadlock from Lock Order
• Test-and-Set Spinlock
• Peterson's Algorithm
• Compare-and-Swap
• Spinlock
• Mutex with a Futex
• Mutex vs Spinlock, side by side
• How a Mutex Works: the Futex
• Readers–Writer Lock
• Read-Copy-Update
• Semaphore
• Semaphore vs Condition Variable
• The Go Scheduler
• OS Threads vs Goroutines
• Inside a Goroutine
• Coroutines: Stackful vs Stackless
• Thread Pool: Java ThreadPoolExecutor
• The Python GIL
• Lock-Free Queue, Michael–Scott
• Barrier and Countdown Latch
• The Actor Model
• Go Channels Inside the Runtime

Computer Architecture 36

• Computer Architecture Mind Map
• Levels of Abstraction in a Computer
• Sequential Logic: Latches, Flip-Flops, Registers and Counters
• A Latch and a Flip-Flop Built from Transistors
• Timing Analysis: Setup, Hold, Clock Skew and Synchronizers
• Finite State Machines: Moore, Mealy, Encodings and Factoring
• Logic Gates: NOT, Buffer, AND, OR, NAND, NOR, XOR, XNOR
• Combinational Logic: Gates, Adders, Muxes and the ALU
• Multilevel Logic, Bubble Pushing, and the Values X and Z
• From Verilog to Hardware: What Synthesis Builds
• Arithmetic Circuits: Fast Adders, Comparators, Shifters, Multiplier
• Number Systems: Two's Complement, Fixed Point and IEEE 754 Floating Point
• Float Formats: FP32 vs FP16 vs BF16 vs FP8
• Memory Arrays: DRAM, SRAM, ROM, Register Files, PLAs and FPGAs
• From C to MIPS Machine Code: Branches, Instruction Formats and Addressing Modes
• Translating and Starting a MIPS Program
• MIPS Procedure Calls: jal, jr $ra, the Stack and Saved Registers
• Building the Single-Cycle MIPS Datapath
• The Single-Cycle MIPS Processor
• How a Program Runs on the MIPS Datapath
• Exceptions in the MIPS Processor
• The MIPS Pipeline: Hazards and Forwarding
• Branch Prediction on the MIPS Pipeline
• Single-Cycle vs Multicycle vs Pipelined MIPS: a Performance Race
• Superscalar and Out-of-Order Execution with Register Renaming
• Parallel Hardware: SIMD, Multithreading and Multicore
• GPU Warps and SIMT: Divergence and Latency Hiding
• How a CPU Cache Finds, Misses and Replaces
• One Load Through the Memory Hierarchy
• DRAM Timing: Why Reading Memory in Order Is Fast
• MESI Cache Coherence and False Sharing
• Virtual Memory in Hardware: Page Table, TLB, Protection and Replacement
• Embedded I/O: Memory-Mapped I/O, GPIO, UART, SPI, Timers and Interrupts
• Register Allocation by Graph Coloring
• RISC vs CISC: One C Line on MIPS and x86-64
• Shift Registers and Counters

Java & the JVM 29

• Java & the JVM Mind Map
• Compiler vs Interpreter
• How a Java Program Is Compiled and Run
• How a Java Application Starts
• HotSpot JIT Tiers
• How V8 Runs JavaScript
• Java Garbage Collectors: Parallel GC, G1, ZGC
• Tracing GC vs Reference Counting
• Stack vs Heap in Java
• Pass by Value vs Pass by Reference: Shallow vs Deep Copy
• How Java's HashMap Works
• How Java's TreeMap Works
• How Java's ConcurrentHashMap Works
• From a Java Thread to a CPU Core
• Java ForkJoinPool and Work Stealing
• Spring Core: IoC Container, Bean Lifecycle, Scopes, AOP Proxies
• Spring MVC Request Flow: DispatcherServlet to Handler to View
• Inside a Tiny Compiler
• Go's Garbage Collector
• How Java Loads a Class
• Java Memory Model: happens-before, volatile, synchronized
• ReentrantLock and AbstractQueuedSynchronizer
• synchronized Lock States: Thin Lock and Inflation
• Python Garbage Collection: Reference Counting and the Cycle Collector
• Java Virtual Threads vs Platform Threads
• Card Table and Write Barrier in HotSpot
• Java Safepoints
• Lambdas and invokedynamic
• Hibernate Session: Persistence Context and Dirty Checking

Machine Learning 63

• Machine Learning Mind Map
• Gradient Descent
• SGD vs Momentum vs Adam
• Linear & Logistic Regression
• L1 vs L2 Regularization
• Bias–Variance Trade-off and Cross-Validation
• Perceptron Learning Rule
• K-Nearest Neighbors
• K-Means Clustering
• Supervised vs Unsupervised vs Reinforcement Learning
• DBSCAN Density Clustering
• k-means vs Gaussian Mixture Model
• PCA vs t-SNE
• Decision Tree Learning
• Random Forest vs Gradient Boosting
• Naive Bayes Spam Filter
• Precision vs Recall
• ROC Curve and AUC
• Neural Network Forward Pass
• Activation Functions: Sigmoid vs tanh vs ReLU vs GELU
• Neural Network: Recognizing Digits
• Backpropagation
• Backpropagation Intuition
• Draw a Digit: Neural Network Math
• Draw a Digit: Template Matching
• Softmax & Cross-Entropy
• Train a Tiny Network on Your Points
• Convolution in a CNN
• CNN vs Transformer: Receptive Field vs Self-Attention
• Residual Connections
• Recurrent Networks: RNN, LSTM and GRU
• Self-Attention
• Encoder–Decoder Attention: How a Transformer Translates
• RoPE: Rotary vs Sinusoidal Position Encoding
• Byte-Pair Encoding
• How a Large Language Model Works
• Decoding Strategies: Greedy vs Beam Search vs Top-p
• LoRA and Quantization
• How an AI Agent Works
• Retrieval-Augmented Generation
• HNSW Vector Search
• MCP: the Model Context Protocol
• BM25 vs Vector Search vs Hybrid
• Diffusion Model
• VAE vs GAN on 2D Points
• Dropout & Batch Normalization
• BatchNorm vs LayerNorm vs RMSNorm
• The KV Cache
• MHA vs GQA vs MQA Attention
• FlashAttention: Tiles in SRAM
• Continuous Batching in LLM Serving
• Logistic Regression
• Mixture of Experts
• RLHF vs DPO
• Speculative Decoding: Draft Model and One-Pass Verification
• Support Vector Machine
• Word2Vec
• Contrastive Learning and CLIP
• Hierarchical Clustering: Merge the Closest Pair
• Weight Initialization: Xavier and He
• Learning Rate Schedules: Warmup and Decay
• Knowledge Distillation
• Matrix Factorization for Recommendations

AI: Search, Games & Reasoning 18

• AI: Search, Games & Reasoning Mind Map
• Uniform-Cost Search vs Iterative Deepening
• Minimax and Alpha-Beta Pruning
• Monte Carlo Tree Search
• Constraint Satisfaction: Backtracking Search
• Forward vs Backward Chaining
• Simulated Annealing
• Travelling Salesman Heuristics
• Genetic Algorithm
• Value Iteration
• Q-Learning in a Grid World
• Bayesian Network Inference
• Viterbi Algorithm: Decoding a Hidden Markov Model
• Multi-Armed Bandit
• Expectimax and Chance Nodes
• Policy Gradient: REINFORCE
• Particle Filter: Robot Localization
• Sampling in a Bayesian Network

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