Sandbox
Interactive visualizations, mathematical proofs, and distributed systems articles.
- What Is a Matroid? A Visual Introduction
An interactive introduction to matroids — the structure that captures the essence of linear and graphical independence, and explains exactly when the greedy algorithm is optimal.
- CSR: How Graphs Are Stored in Flat Arrays
Interactive visualization of Compressed Sparse Row — three flat arrays that replace nested hash maps for sparse graph storage, with 10-30x speedups from cache locality alone.
- Pythagorean Theorem: Visual Proof
An interactive visual proof of the Pythagorean theorem using area rearrangement of four identical right triangles inside a square.
- Proof that √2 is Irrational
Interactive step-by-step proof by contradiction that the square root of 2 cannot be expressed as a ratio of two integers.
- Cantor's Diagonal Argument: ℝ is Uncountable
Interactive visualization of Cantor's diagonal argument proving that the set of real numbers is uncountable — there is no bijection between ℕ and ℝ.
- Apache Spark RDD Transformations Pipeline
Interactive visualization of how Apache Spark RDD transformations form a lazy evaluation pipeline — map, filter, and reduce operations on distributed data.
- Spark Fault Tolerance via RDD Lineage
Interactive visualization of how Apache Spark recovers from executor failures using RDD lineage — recomputing lost partitions from their transformation history.
- Spark DAG Scheduler: From Logical Plan to Physical Execution
Interactive visualization of how Spark's DAG scheduler converts a logical plan into stages and tasks, performing topological sort and stage boundary detection at shuffle points.
- EMR YARN Dynamic Executor Allocation
Interactive visualization of how Amazon EMR with YARN dynamically scales Spark executors up and down based on workload demand, balancing resource utilization and cost.