Encode chaotic dynamics as symbol sequences. Visualize sofic shifts, subshifts of finite type, de Bruijn graphs, and compute topological entropy h = log(spectral radius of transition matrix).
Symbolic dynamics: partition phase space into symbols. Orbit maps to infinite sequence. Subshift of finite type (SFT): defined by forbidden words. Topological entropy h_top = lim_{n→∞} (1/n) log|L_n| = log λ_max (Perron-Frobenius eigenvalue of transition matrix). Golden mean shift: forbidden "11" → λ=φ=(1+√5)/2, h=log φ. Sofic shifts: images of SFTs under 1-block codes (Fischer 1975). Connection: Markov partitions (Sinai, Bowen 1970s) allow symbolic coding of Anosov flows.