Quadratic Julia Sets & Mandelbrot Set

graph TD DefFc["Def: Quadratic family\nf_c(z) = z² + c"] DefKc["Def: Filled Julia set K_c\n{z : orbit bounded}"] DefJc["Def: Julia set J_c\n= ∂K_c"] DefM["Def: Mandelbrot set M\n{c : 0 ∈ K_c}"] LemCrit["Lem: Critical point 0\nOnly critical point"] ThmEquiv["Thm: M = {c : K_c connected}\nDouady-Hubbard"] ThmCompact["Thm: M compact\nM ⊆ D(0,2)"] DefParam["Def: Parameter space\nc-plane"] DefDyn["Def: Dynamic plane\nz-plane, f_c iteration"] DefFc --> DefKc DefFc --> DefJc DefKc --> DefJc DefKc --> DefM LemCrit --> DefM DefM --> ThmEquiv DefM --> ThmCompact DefFc --> DefParam DefFc --> DefDyn classDef definition fill:#b197fc,color:#fff,stroke:#9775fa classDef theorem fill:#51cf66,color:#fff,stroke:#40c057 classDef lemma fill:#74c0fc,color:#fff,stroke:#4dabf7 class DefFc,DefKc,DefJc,DefM,DefParam,DefDyn definition class ThmEquiv,ThmCompact theorem class LemCrit lemma