Lorenz Solver

This applet solves the Lorenz equations and the corresponding Lyapunov exponents and dimension. σ, b, and r are equation parameters; x0, y0, and z0 are the initial conditions; dt is the time step; and t-max gives the duration of the calculation (the time unit at the end of the computation). Norm. step-time sets the number of time units between normalizations in calculating Lyapunov exponents. Norm. wait time gives the time units of warm-up time in calculating Lyapunov exponents (normalizations occurring without drawing exponents). Pressing Restart will recalculate the system with any changes to these options. Pressing the Track button will display a point that follows the system solution through time. The Track-rate slider changes how fast the point moves. λ1, λ2, and λ3 are the respective first, second, and third Lyapunov exponents describing the exponential rate of divergence from infinitesimally close conditions. D is the Lyapunov dimension, describing the complexity of the chaos. Graph selections Z-X, Y-X, and Z-Y display projections of the the Lorenz attractor. λ1t-t and the next two graph options display the set of instantaneous first, second, and third Lyapunov exponents respectively. λ1-t and the next two graph options display the time averaged value of the first, second, and third Lyapunov exponents respectively. D-t displays the time averaged value of the Lyapunov dimension. Pressing the Box-Count button, calculates the box-counting dimension and displays the dimension value for each mesh increment. Increasing increment corresponds to smaller box sizes. The Lorenz equations are

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