Chapter 10: Processes of Perception and Analysis

Section 1: Introduction

Section 2: What Perception and Analysis Do

Section 3: Defining the Notion of Randomness

Algorithmic information theory History [of randomness definitions] Inevitable regularities and Ramsey theory

Section 4: Defining Complexity

History [of complexity definitions]

Section 5: Data Compression

Practicalities [of data compression] History [of data compression] Number representations Lengths of [number] representations Completeness [of number representations] [Number representations in] practical computing Run-length encoding Huffman coding Maximal block compression Arithmetic coding Pointer-based encoding LZW algorithms Recursive subdivision [encoding] 2D run-length encoding

Section 6: Irreversible Data Compression

History [of irreversible data compression] Orthogonal bases Walsh transforms Walsh spectra Hadamard matrices Image averaging Practical image compression Fourier transforms JPEG compression Wavelets Sound compression

Section 7: Visual Perception

Color vision Nerve cells The visual system Feedback [in visual processing] Scale invariance [in vision] History [of vision research] Implementation [of texture perception model] Testing the [texture perception] model Related [texture perception] models Image processing Real textures Statistical methods [for texture analysis] Camouflage Halftoning Generating textures Moire patterns Perception and presentation

Section 8: Auditory Perception

Sounds Auditory system Chords History [of auditory perception] Sonification Implementation [of sound] [Sounds based on] time variation [Sounds based on] musical scores Recognizing repetition [in sounds] Sound compression Spectra [of sequences] Spectra of substitution systems [Sequences with] flat spectra Nested vibrations [Spectra of] random block sequences Spectra of cellular automata 2D spectra Diffraction patterns

Section 9: Statistical Analysis

History [of statistics] Practical statistics Time series Origin of probabilities Probabilistic models Binomial distribution Estimation of parameters [in probabilistic models] Complexity of models Markov processes [Models involving] non-local processes Block frequencies [in sequences] LFSR sequences Entropy estimates [for sequences] Tests of randomness Difference tables Randomized algorithms

Section 10: Cryptography and Cryptanalysis

History [of cryptography] Basic theory [of cryptography] [Redundancy in] text Cryptanalysis Linear feedback shift registers LFSR cryptanalysis Rule 30 cryptography [Cryptographic] properties of rule 30 Directional sampling [in cellular automata] Alternative rules [for cryptography] Nonlinear feedback shift registers Backtracking [in cellular automata] Deducing cellular automaton rules [Cryptanalysis of] linear congruential generators Digit sequence encryption Problem-based cryptography Factoring integers RSA cryptography Quadratic residue sequences

Section 11: Traditional Mathematics and Mathematical Formulas

Practical empirical mathematics Difference tables and polynomials Implementation [of repetitive array] Nested patterns and numbers Implementation [of finite automata for nested patterns] [Patterns from] arbitrary digit operations Generating functions [for nested patterns] Pascal's triangle Nesting in bitwise functions Trinomial coefficients Gegenbauer functions Standard mathematical functions [Generating functions for] 1D sequences Multidimensional additive rules Continuous generalizations [of additive rules] Nested continuous functions GCD array Power cellular automata Computing powers [of numbers] Complex powers [of numbers] [Algebraic computation of] additive cellular automata The more general case [of computation speed ups] Evaluation chains Boolean formulas DNF minimization [Boolean] formula sizes Cellular automaton [Boolean] formulas Primitive [Boolean] functions Multilevel [Boolean] formulas Nand expressions Cellular automaton [Nand] formulas Binary decision diagrams History [of Boolean functions] Reversible logic [Reduced formulas in] continuous systems

Section 12: Human Thinking

The brain History [of ideas about thinking] The future [of machine thinking] Sleep Pointer encoding [and memory] Hashing [Identifying] similar words [Memory analogs with] numerical data Error-correcting codes Matrix memories Neural network models [Human] memory [Cognitive] child development Computer interfaces Context-free languages [Computer and human] languages Computer language fluency Brainteasers Human generation of randomness Game theory Games between programs

Section 13: Higher Forms of Perception and Analysis

Biological [forms of] perception Evolving to predict [data] Familiar features [of perceived data] Relativism and postmodernism

From Stephen Wolfram: A New Kind of Science [citation]