Bloom Filter: Probabilistic Set Membership

A Bloom filter answers "have I seen this before?" using a fixed-size bit array and several independent hash functions, trading a small, tunable chance of false positives for constant-time inserts and queries with no false negatives ever. This simulator renders the bit array as a ring of spheres in 3D — insert words to watch k hash functions light up bits across the ring, query any word to see whether the filter reports it present, and run a batch of false-positive trials to compare the measured error rate against the exact theoretical formula that governs every real Bloom filter in production.