Chaos Random Numbers Chaos 1D Logic Map 1d chaotic logic map x n 1 u x n 1 x n for a range of system parameters u and starting values x x 0 starting value 0 to 1 u system parameter behaviour 0 to 4 Randomness u values in the range of approximately 3 57 to 4 0 exhibit chaotic behavior DOCTYPE html html lang en head meta charset UTF 8 meta name viewport content width device width initial scale 1 0 title 1D Chaotic Logistic Map title script src https cdn plot ly plotly latest min js script head body div id plots div script Example parameters const uValues 2 5 3 5 3 999 3 58 const x0Values 0 1 0 5 0 9 0 5 const iterations 100 const plotsContainer document getElementById plots Plot for each combination of parameters for let k 0 k uValues length k const u uValues k const x0 x0Values k const title Logistic Map u u x0 x0 const plotDiv document createElement div plotDiv style width 600px plotDiv style height 400px plotsContainer appendChild plotDiv const data generateData u x0 iterations title const layout title title Plotly newPlot plotDiv data layout Function to generate plot data function generateData u x0 iterations title let x x0 const xValues const yValues for let i 0 i iterations i const nextX u x 1 x xValues push i yValues push nextX x nextX const trace x xValues y yValues mode lines name title return trace script body html
const title Logistic Map u u x0 x0 const plotDiv document createElement div plotDiv style width 600px plotDiv style height 400px plotsContainer appendChild plotDiv const data generateData u x0 iterations title const layout title title Plotly newPlot plotDiv data layout Function to generate plot data function generateData u x0 iterations title let x x0 const xValues const yValues for let i 0 i iterations i const nextX u x 1 x xValues push i yValues push nextX x nextX const trace x xValues y yValues mode lines name title return trace script body html