Chaos Demonstrations Changes from Version 1.0 to Version 1.1 Created May 1, 1990 1. The CHAOS.PIF file has been modified so that the program launches 3 seconds faster from Windows. 2. The label "MS-DOS Version" has been changed to "IBM PC Version." 3. Ordering information has been removed from the logo screen. 4. The Num Lock is turned off so the arrow keys on the numeric keypad work, and the original Num Lock state is restored upon exit from the program. 5. The Poincare sections now show x versus v at constant phase of the drive rather than v versus the previous v at x=0, and what was previously called a Poincare section is now called a return map. 6. The Poincare sections continue to develop beyond the previous limit of about 32,000 points. 7. The return map calculates faster in the Driven Pendulum demonstration. 8. A distortion of the Three-body Problem during zoom has been corrected. 9. The Van der Pol Equation now shows all 15 trajectories with any background color in CGA mode. 10. The scale has been changed to enlarge the Lorenz Attractor. 11. The Lorenz attractor now has initial values that lie on the attractor for the default parameters. 12. The Logistic Map no longer erases the screen at the end of the plot but rather retraces itself with increased accuracy. 13. The step size on the parameters I and L in the Logistic Map has been reduced from 0.2 to 0.1. 14. A track/untrack option has been added to the Logistic Map. 15. An error in the labeling of the Predator-Prey has been corrected. 16. The Henon Map now continues counting iterations beyond 32,767. 17. The number of points in the Henon Map is now adjusted according to the amount of free memory and the graphics mode in use. 18. An error in the calculation of D under some conditions in the Diffusion demonstration has been corrected. 19. The fractal dimension is now shown for all fractals. 20. A problem with cycling among views of the Deterministic Fractals has been corrected. 21. The cursor now responds while the snowflake fractal is being drawn. 22. A triadic Cantor set has been added to the Deterministic Fractals. 23. The Random Fractal calculates slightly faster and grows more symmetrically to fill the entire screen and changes color less often. 24. The Game of Life no longer stops at 32,767 generations. 25. Some labels have been changed in some of the individual views, including spelling out words that were previously abbreviated. 26. A problem with the screen not fully erasing in the zoom mode has been corrected. 27. Some colors have been changed to improve legibility. 28. More background color choices are available when running in the monochrome VGA graphics mode with a color monitor. 29. A problem when running the program with a CGA card on some early vintage PC's has been corrected. 30. The program now works properly with a monochrome Hercules graphics adapter. 31. The program now works properly in MODE MONO with a VGA. 32. A change in graphics mode or color in one demo remains in effect for all demos except while in the museum (recycle) mode. 33. Some unnecessary screen blinking in the recycle mode has been eliminated. 34. Some changes have been made in the AUTO.TXT file that controls the recycle sequence. 35. A problem with the screen sometimes not erasing when the user takes over in the museum mode has been corrected. 36. A new command (;) has been added that dissolves (fades on VGA) the screen display. 37. The key now can be used to single-step through the auto-cycle sequence. 38. Data from the calculations can now be saved to a disk file by adding {filename} to the CHAOS command string. 39. The user can now create a log of computer use in a disk file by starting the program with a command such as CHAOS {filename}R. 40. When the command string begins with an E or Z, the program bypasses the initial screen. 41. A problem with the recycle sequence sometimes stopping at midnight has been corrected. 42. Abbreviations and periods have been eliminated from the quiz text. 43. Skipped questions now count against the score in the quiz. 44. The explanation screens have some additions and rewording and are no longer right-justified. 45. Some rare numeric errors have been corrected. 46. The CHAOS.EXE file is now about 11K longer, but the program still requires at most only 200K of free memory. 47. Error trapping, especially for out-of-memory conditions, has been improved. 48. A problem with the mouse cursor when using a Logitech mouse driver Version 3.4 has been corrected. 49. The help text is now displayed as white on blue instead of green on black, and the cursor controls on the help screen are shown in reversed colors. 50. The README.DOC file has been renamed to HELP.TXT and revised to reflect the above changes. Changes from Version 1.1 to Version 2.0 Created September 10, 1991 1. The screen dissolve rate is now CPU independent (on fast machines). 2. README.DOC has been renamed to README.TXT. 3. A more compact version of MENUDRVR.EXE has been used, and it has been renamed to PASDRVR.EXE. 4. Axes are labeled on the graphs in the conventional way. 5. The current view is now indicated in the command box. 6. Phase-space plots in the Pendulum and Nonlinear Oscillator demos are now easier to see. 7. The Pendulum now has a velocity-versus-time view. 8. The Pendulum now allows control over the damping. 9. A problem with a missing cursor in the quiz with no mouse has been fixed. 10. A minor error in the mean of the 1/f Noise demo was corrected. 11. A rare overflow error in the Pendulum demo has been corrected. 12. The plotting rate is now CPU independent (on fast machines) where appropriate. 13. The calculation speed has been significantly increased in many demos. 14. The sound quality has been improved on those demos with sound. 15. Deterministic fractals now include a fractal tree, a Hilbert curve, a devil's staircase, Cantor curtains, Sierpinski carpet, Von Koch island, flat Fournier universe and a 3-D tree. 16. Launching the program with certain commands such as CHAOS,R no longer freezes up the computer. 17. The views in the Logistic Map demo have been reordered. 18. The letter for each demo rather than the name is now stored in the museum LOG.USE file to reduce disk space and disk access time, and the museum log now shows all demos that were viewed rather than just the first. The time in use no longer records negative values when use extends through midnight. 19. Many of the explanation screens have been reworded. 20. Zero is now an acceptable delay in the command string. 21. The Pendulum and Nonlinear Oscillator now have a Poincare movie view. 22. Text screens are now allowed between quotes in the command string. 23. The output of the most recently viewed demonstration can now be saved by placing the output filename in curly brackets as the first item in the command string. 24. The Nonlinear Oscillator has been modified to include the same features as the Pendulum demo. 25. Minor inaccuracies in the Pendulum and Nonlinear Oscillator have been corrected. 26. The initial condition is now on the attractor in the Pendulum and Nonlinear Oscillator demos. 27. A Duffing Oscillator demonstration has been added. 28. Some minor cosmetic changes have been made. 29. The Lorenz Attractor demo has been completely rewritten with seven new views. 30. A Rossler Attractor demonstration has been added. 31. A "Magnify" command has been added to many of the demos. 32. The Logistic Map demo has been renamed to One-Dimensional Maps, and five other maps have been included. 33. A more accurate integration scheme is now being used in the Pendulum, Nonlinear Oscillator and Van der Pol Equation demos. 34. A more accurate interpolation scheme is now being used for the return maps in the Pendulum and Nonlinear Oscillator demos. 35. The range of L accessible to the user has been expanded in the One- Dimensional Maps demo. 36. The divergence of the two initial conditions in the One- Dimensional Maps demo is now plotted on a semilog graph, and the initial conditions now differ by only one part in 108. 37. The quiz now has four extra questions (1 for each additional demo). 38. The range of available b values has been increased in the Henon Map, and the default b has been changed from 0.4 to 0.3. 39. The Henon map now has a view of the basin of attraction. 40. The Noise demo now erases as it plots rather than at the end of the sweep. 41. A problem with the noise demo sometimes plotting outside the window has been corrected. 42. Five new views have been added to the Julia sets demo. 43. The <+> and <-> keys can be used to cycle among the 64 color palettes on EGA and VGA monitors. 44. Initial velocities in the Three-Body demo now differ by 1% rather than 10%. 45. Stereoscopic 3-D views have been added to the Pendulum, Nonlinear Oscillator, Duffing Oscillator, Magnetic Quadrupole, Lorenz Attractor, Rossler Attractor and Deterministic Fractals demonstrations. 46. The user now has access to the program menu from the museum mode by pressing . 47. The space bar no longer unzooms the display or exits the explanation screen when in the auto mode. 48. now replicates the function of the key. 49. The autoscript can now be read from an arbitrary file by starting the program with a command such as CHAOS (MYSCRIPT.TXT). 50. The particle trajectory no longer erases the field lines in the magnetic quadrupole demonstration. 51. Some quirks in the behavior of the DOS shell have been corrected. 52. A fancier screen wipe has been added. 53. A problem with the Chirikov map sometimes plotting out of bounds has been corrected. 54. A 3-D view has been added to the diffusion demonstration, and the maximum number of particles has been increased from 256 to 512. 55. A Cellular Automata demo has been added. 56. An Anaglyphs demo has been added. 57. The keyboard buffer no longer overflows when certain keys are held down. 58. The menu cursor position is now remembered and restored between demos. Changes from Version 2.0 to Version 3.0 Created November 19, 1994 1. The program has been recompiled with PowerBASIC 3.0 rather than TurboBASIC 1.1, causing the program to run up to three times faster, however, necessitating that the program run under DOS 3.0 or higher. 2. The VGA screen fade is now faster and smoother. 3. The anaglyphs now rotate more smoothly on fast machines. 4. A Strange Attractors demo has been added. 5. An Iterated Function Systems demo has been added. 6. A Coupled-Map Lattice demo has been added. 7. A Mixing demo has been added. 8. A Percolation demo has been added. 9. The Weierstrass Function demo has been moved to view 8 of the Deterministic Fractals demo. 10. The Quiz and Auto modes have been expanded to include the new demos. 11. All graphics modes now have a highlighted cursor. 12. The Mandelbrot and Julia sets now compute faster, show more detail, use a different color scheme, and include magnify and pan options. 13. The Julia Set demo now includes views of Lakes, Esses, Whirls, and Spirals. 14. A problem with the computer sometimes hanging up when the keyboard buffer fills and the sound is on has been corrected. 15. A fractal word, Cantor maze, twin dragon, Julia dendrite, maple leaf, Peitgen tree, and Sierpinski tetrahedron view have been added to the Deterministic Fractals demo. 16. The Deterministic Fractals demo labels and dimensions are now visible when the screen is zoomed. 17. It is now possible to cycle backwards as well as forward with the Graphics, Color, View, Magnify, Rotate Palette (<-> and <+>), and Parameters commands by simultaneously pressing the key or by using lower-case characters in the command sequence. 18. Illegal commands on the menu screen now produce a chirp. 19. The game of life has improved graphics, calculates much faster, uses periodic boundary conditions, and allows the user to choose from among 2025 different rules, rather than just the single classic rule. 20. The Van der Pol Equation demo now includes an optional sinusoidal drive term, which produces entrainment, quasiperiodicity, and chaos, and negative values of h are allowed to illustrate a repellor. 21. The One-Dimensional Map demo now includes a quartic map, square- root map, Bernoulli map, circle map, sine-circle map, May map, and a cusp map. 22. The One-Dimensional Map demo now includes a view of the probability distribution. 23. The colors have been changed in the One-Dimensional Map demo to improve legibility. 24. The function keys F1 through F3 can now be accessed from anywhere in the program. 25. The Chirikov Map demo now allows for the addition of dissipation. 26. The explanation screens have been edited to reflect the changes. 27. Graphics screens can now be printed using the ^ command in the command sequence, which is the same as pressing the key. 28. A problem with command delays sometimes being ignored has been corrected. 29. The color palette rotation (with the <+> and <-> keys) is now smoother (some colors were previously out of order). 30. A timing problem when the program is launched from Windows has been corrected. 31. The Three-Body Problem, Magnetic Quadrupole, and Diffusion demos now allow up to 1024 particles depending upon available memory. 32. Memory exhaustion is now handled more gracefully. 33. The Henon Map demo now includes more points (depending on available memory and CPU speed), allows negative values of b, and corrects a previous problem with points on the attractor sometimes appearing outside the basin of attraction. 34. The Menu Driver has been revised to support an equipment list on the PASDRVR command line, and this feature is used to verify that the computer has at least DOS 3.0 and 384K of RAM. 35. In the Cellular Automata demo, the plot has been reoriented so that time advances downward, the parameters can now go up to 256 (rather than 64), the parameter M has been relabeled k, and two new views have been added in which the initial conditions are random rather than periodic. 36. "IBM PC Version" has been changed to "PC Version". 37. Data files are loaded much faster, especially from floppy disks. Changes from Version 3.0 to Version 3.1 Created June 28, 1995 1. The Mandelbrot and Julia set programs now include a Track/Untrack option that maps the escape time to colors using either a (base-2) logarithmic or linear scale, respectively. 2. The parameters for some of the Julia sets have been changed slightly to produce more structure at high magnification. 3. The Julia set program now includes a view that does a random search for interesting parameter sets. 4. Typing "CHAOS /?" or "CHAOS /HELP" from the DOS prompt now brings up the program name, version, and command-line syntax. 5. The program has been recompiled with version 3.1 of PowerBASIC. 6. The copyright date has been changed from 1994 to 1995. 7. A rare overflow error in the Nonlinear Oscillator has been corrected. 8. The wording of some of the explanation screens has been clarified. 9. Pressing R now resets the original initial conditions in the Lorenz and Rossler Attractor demos. 10. A URL for the author's World Wide Web page has been included in HELP.TXT 11. The phrase "Use colored glasses" has been changed to "Use colored graphics" when the user is viewing an anaglyph in a monochrome graphics mode. Changes from Version 3.1 to Version 3.2 Created January 1, 1998 1. A problem with the sound hanging on and the program crashing with certain brands of computers has been corrected. 2. The command line help function now gives improved instructions. 3. The colors can now be cycled forward or backward on computers with keyboards without keypads. 4. The Strange Attractor and IFS searches now cycle about twice as fast as before, producing a new image every 5-10 seconds on average. 5. The logo screen no longer appears while the program is loading on fast machines with coprocessors. 6. An icon file (CHAOS.ICO) has been provided for the convenience of Windows users. 7. The 1-D maps now allow a wider range of the A parameter, and an error in some of the bifurcation diagrams and Lyapunov exponent plots has been corrected. 8. Missing ancillary .TXT files do not delay loading or operation of the program. 9. The left mouse button now emulates the space bar in a script that is waiting for a keyboard command to advance to the next screen. 10. The directory text screen colors have been changed to white on blue. 11. A CHAOS.HTM file has been added to simplify launching the program from a Web browser and to provide links to Web resources. 12. Error messages now appear in a dialog box with an OK button. 13. The program has been recompiled with PowerBASIC 3.5. 14. The Anaglyph and other animations have been synchronized with the monitor vertical retrace to minimizing strobing. 15. Six more Julia Set views have been added. 16. A problem with the mouse buttons not resetting when the program is launched has been corrected. 17. The Random Fractals, Diffusion, and IFS demos now have labels at the bottom of the screen in zoom mode.