| Name | Modified | Size | Downloads / Week |
|---|---|---|---|
| Parent folder | |||
| Readme.txt | 2020-10-21 | 3.2 kB | |
| Astroid.asm | 2020-10-21 | 5.1 kB | |
| Cardioid.asm | 2020-10-21 | 5.1 kB | |
| Totals: 3 Items | 13.4 kB | 0 | |
============================ The "Astroid" Curve =============================== This curve is derived by drawing a line of fixed length between many positions on the a pair af adjacent axes ( regard the line as sliding between fixed the constaints of the axes). The envelope generated by the series of line created in this way is an Astroid curve. 14/10/03 ============================ The "Butterfly" Curve ============================= This is a graphic example of curve construction using polar coordinates using an the equation given in an article by T.Fay, American Math Monthly. 96(5): 442-443 23/05/99 ============================ The "Cardioid" Curve ============================== This is a geometric construction in which a base circle (not shown) provides a target for a series of cicles to be drawn on its circumference. The location of the circle centres is determined by rotating the base cicle radius though 5 degree intervals until a full rotation of 360 degrees is reached; each intersection of the radius with the circumference marks the centre of a new circle with radius of length equal to to the distance to the initial starting point of the series. The envelope generated by the series of circles generated in this way is a Cardioid curve. The pattern shown is quite beautiful in its own right, but if you want to construct a bare cardioid cureve then you can do this by using the polar equation: r = 2a(1-cos(theta)) where r is the radius theta is the angle and the base circle radius is 4a 20/10/03 ============================ Feigenbaum Diagram ================================ This example illustrates Feigenbaum's period doubling demonstation of the onset of chaos. Refer to "Chaos and Fractals" by Peitgen, Jurgerns and Saupe if you want to delve into this interesting branch of mathematics. 19/05/99 ============================ The Fern Fractal ================================== This is a classic fractal which illustrates the existance of fractal objects in everyday life. It is generated as an Iterated Function System (IFS). 23/05/99 ============================ The Ikeda Attractor =============================== This is graphical demo which reproduces the clasic "Ikeda Attractor". Try resizing the window and you will see a completely different orbit each time! 15/05/99 ============================ The Lorenz Attractor ============================== This is graphical demo which reproduces the clasic "Lorenz Attractor". It solves three differential equations to compute the orbit created by the chaotic attractor. Try resizing the window and you will see a completely different orbit each time! 15/05/99 ============================ The Rosler Attractor ============================== This is graphical demo which reproduces the clasic "Rosler Attractor". It solves three differential equations to compute the orbit created by the chaotic attractor. Try resizing the window and you will see a completely different orbit each time! 15/05/99 Enjoy Ron Thomas Ron_Thom@Compuserve.com www.rbthomas.freeserve.co.uk
