IFS Animations

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L2h1.mov -- L. Riddle

Here, the Levy dragon is continuously transformed into the Heighway dragon. (Do you see the twindragon at the half-way point?)

L2h1.mov   

rectri.mov --- Aug 28, 1992

As the parameters in an iterated function system are changed, the resulting attractor changes (continuously). Here is an example of that, a rectangle that changes into a triangle. We follow the curved edge in the upper left of the Mandelbrot-type set in Figure VIII.237 of Barnsley's Fractals Everywhere, Academic Press (Figure 8.4.1(a) in the first edition).

The individual frames were computed by "Fractal Attraction" (Addison-Wesley), then made into a movie with Apple's Quicktime software.

rectri.mov   

third.mov --- Sept 9, 1992

As the parameters in an iterated function system are changed, the resulting attractor changes (continuously). Here is an example of that, based on two non-commuting affine transformations:

   (T1)    x' =  (1/3) x + (1/3) y
           y' =            (1/3) y

   (T2)    x' =  (1/3) x           + e
           y' =  (1/3) x + (1/3) y + f

We watch what happens as the point (e,f) moves around a circle. [ref: Suppl. Rend. Circ. Mat. Palermo 28 (1992) p. 350.]

The individual frames were computed by "Fractal Attraction" (Academic Press), then made into a movie with Apple's QuickTime software.

third.mov   

poly.mov -- Sept 15, 1992

As the parameters in an iterated function system are changed, the resulting attractor changes (continuously). This one is called (for reasons I cannot explain here) Polymer.

The individual frames were computed by "Fractal Attraction" (Academic Press), then made into a movie with Apple's QuickTime software.

Poly.mov   

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