| Order version 4 replaces version 3.2 with a program designed for the Windows 95 through Windows XP operating systems. The operator interface and the mathematical models have been completely re-worked. This is a whole generation ahead of Order 3.2, our classic introduction to the mathematics of chaos. Imagine a textbook in which the illustrations were working models of the mathematical or physical objects being studied. The reader would have the ability to alter the parameters that define the object so as to see immediately the effect. It would be an excellent way to gain understanding of the subject and build that intuition that allows a student to go beyond what is covered in a classroom and really own the material. Now let's imagine that in this textbook the text may be edited, added to or written from scratch by the reader and that new models may be created to illustrate the principles expounded in the text... and that these new models may be studied and modified by future readers. This is the paradigm upon which we base our run-time books, including the virtual laboratory in the book as embedded mathematical models. Order is such a run-time book. The text includes the following topics: - Numbers Functions and Graphs
- Iteration and Attractors
- Phase-Control Maps
- Complex Numbers and Functions
- Mandelbrot and Julia Sets in the Complex Plane
- Fractal Image Generation by Iteration of Linear Transforms
- Duffing Mechanical Oscillator
- Phase Space Orbits
- Phase Space Orbit Sections
- Bains of Attraction
The run-time technology that powers Order is a next logical step in computer-aided education. In the beginning there were printed textbooks with static pictures and graphs that just lay there on the page. Then there were computer-aided texts that were basically just electronic page-turners. Next came multi-media presentations where animation, video, audio and all sorts of snappy pictures were presented along with the text. Even the slickest multi-media presentation though is frozen at the time the program is produced, at compile-time, as the programming people say. All the reader can do is choose a path through material that has been prepared for her. When our book programs are running, at run-time as it were, the reader can get into the underlying algorithms and make changes to the displays that serve as our illustrations, fundamentally changing the program as it runs to illustrate ideas that the author may not have thought of. Practically infinite variation is possible. |
