Dynamics: Numerical Explorations

Preface 1. Getting the program running 1.1 The Dynamics program and hardware Smalldyn: a small version of Dynamics 1.2 Getting started with Dynamics Using the mouse Appendix: description of the interrupts 1.3 Questions 2. Samples of Dynamics: pictures you can make simply 2.1 Introduction Example 2-1a: Plot a trajectory Example 2-1b: Draw a box Example 2-1c: Viewing the Parameter Menu Example 2-1d: Refresh the screen and continue plotting Example 2-1e: Clear the screen and continue plotting Example 2-1f: Single stepping through a trajectory Example 2-1g: Plot a cross at current position Example 2-1h: Draw axes and print picture Example 2-1i: Initializing Example 2-1j: Viewing the Y Vectors Example 2-1k: Find a fixed point Example 2-1l: Find a period 2 orbit Example 2-1m: Search for all periodic points of period 5 Example 2-1n: Change RHO Example 2-1o: Plotting permanent crosses Example 2-1p: Set storage vector y1 and initialize Example 2-1q: Change X Scale or Y Scale 2.2 Complex pictures that are simple to make Example 2-2a: Chaotic attractor Example 2-2b: Computing Lyapunov exponents Example 2-2c: Plotting trajectory versus time Example 2-3a: Graph of iterate of one dimensional map Example 2-3b: Cobweb plot of a trajectory Example 2-3c: Plotting trajectory versus time Example 2-4: The Henon attractor Example 2-5: The first iterate of a quadrilateral Example 2-6: Plotting direction field and trajectories Example 2-7: Bifurcation diagram for the quadratic map Example 2-8: Bifurcation diagram with bubbles Example 2-9: All the Basins and Attractors Example 2-10: Metamorphoses in the basin of infinity Example 2-11: Search for all periodic points with period 10 Example 2-12: Search for all period 1 and period 2 points Example 2-13: Following orbits as a parameter is varied Example 2-14: The Mandelbrot set Example 2-15: All the Basins and Attractors Example 2-16: 3-Dimensional views on the Lorenz attractor Example 2-17: Unstable manifold of a fixed point Example 2-18: Stable and unstable manifolds Example 2-19a: Plotting a Saddle Straddle Trajectory Example 2-19b: The unstable manifold of a fixed point Example 2-19c: The stable manifold of a fixed point Example 2-19d: Saddle Straddle Trajectory, and manifolds Example 2-20: The basin of attraction of infinity Example 2-21: A trajectory on a basin boundary Example 2-22: A BST trajectory for the Tinkerbell map Example 2-23: Lyapunov exponent bifurcation diagram Example 2-24: Chaotic parameters Example 2-25: Box-counting dimension of an attractor Example 2-26: Zooming in on the Tinkerbell attractor Example 2-27: Period plot in the Mandelbrot set Appendix Commands for plotting a graph Commands from the Numerical Explorations Menu Plotting multiple trajectories simultaneously 3. Screen utilities 3.1 Basic screen features (Screen Menu SM) Commands for clearing the screen Commands for controlling the screen Level of Text output Writing on pictures 3.2 The arrow keys and boxes (BoX Menu, BXM) 3.3 Initializing trajectories, plotting crosses, drawing circles and their iterates (Kruis Menu KM) 3.4 Drawing axes (AXes Menu AXM) 3.5 Windows and rescaling (Window Menu WM) Detailed view on the structure of an attractor 3.6 Zooming in or zooming out (ZOOm Menu ZOOM) 3.7 Setting colors (Color Menu CM and Color Table Menu CTM) Color screens Core copy of the picture Color planes Commands for erasing colors 4. Utilities 4.1 Setting parameters (Parameter Menu PM) 4.2 Setting and replacing a vector (Vector Menu VM) Y Vectors 'Own' and the coordinates of yÄÜ 4.3 Setting step size (Differential Equation Menu DEM)4.4 Saving pictures and data (Disk Menu DM) Creating a batch file of commands Commands for reading disk files 4.5 Setting the size of the core (Size of Core Menu SCM) 4.6 Printing pictures (PriNter Menu PNM) Commands for specifying printer Encapsulated PostScript Commands for printer options Text to printer Printing color pictures Text to printer Printing color pictures Printing pictures with any