Entropy & Information Studio
Shannon entropy, frequency distributions, redundancy, information limits, gzip-size estimates and first-order conditional entropy.
01 · Input & analysis controls
Analyze text or a file; calculate Shannon entropy and compression ratio estimates.
02 · Information metrics
Entropy, theoretical coding limit, redundancy and compression estimate.
03 · Frequency table
Count, probability, self-information and cumulative probability.
04 · Conditional entropy & entropy rate
For byte streams, estimate H(next byte | previous byte) using adjacent pairs.
05 · Min-entropy & randomness test battery
Rényi entropy chain (H₀ ≥ H₁ ≥ H₂ ≥ H∞), a conservative min-entropy bound, and NIST SP 800-22-style tests (frequency, block frequency, runs, longest run, cumulative sums) plus byte chi-square, serial correlation and Monte-Carlo π. Uses the text or file from panel 01.
06 · Context entropy & sliding window
How much does knowing the previous k bytes help? Shows in-sample plug-in entropy and an honest adaptive-coding cost per order, plus an entropy profile along the input.
07 · Compression & Huffman lab
gzip / deflate / raw deflate sizes, the exact Huffman code for the symbol distribution (verified by encode → decode round trip) and how close it gets to the Shannon limit.
08 · Distribution comparison & language guess
Compares the panel-01 input (A) with another text or file (B): cross-entropy, KL and Jensen–Shannon divergence, cosine similarity. Also estimates the language of A from letter frequencies.
09 · Information-theory calculator
Enter probabilities or counts; or a joint table for mutual information; or a channel parameter for capacity.