Enable Animation

[VittorioAccomazzi]

enable animation in the Julia fractals. Possibilities to explore :

• generating random variation of the C value which was randomly selected.
• generating random path between C values which have been extracted.

[VittorioAccomazzi]

C Point

The current set of C point selected as seed is the following : the point are mostly isolated and not connected. Some of them don't have any neighboured in a large radius.

Possible algorithm :

• Given a point C find all the points within a radius
• select a random one, or select the one towards the center
• if no points are available

[VittorioAccomazzi]

First Attempt

the first attempt is not satisfactory, because there is no continuity across the animation. However does show that the approach is correct : the animation are on average nice.

[VittorioAccomazzi]

Second attempt

In the second attempt I keep finding C point randomly in the same neighbour. The animation is smooth and there are no abrupt changes, however after a wile it is ripetitive, since the C stays in the same area over and over again. So you are not able to experience the different type of Julia types.

[VittorioAccomazzi]

Third Attempt

Attempt to find a path which walks around the Mandelbrot set. In theory this should provide variation on the animation being generated as well as continuity.

In order to find the path I can use the Dijkstra's algorithm, in a pre-processing step. And then at runtime variate the point selected.

The picture below shows in light blue the point in the path. During the animation for each point in the path, a nearby point is selected as target. All these points are shown in dark blue.

the animation which is generated is very smooth and also varies a lot, it effectively shows all type of Julia fractals in available :

The only issue that I see is that the fractal tend to have a large convergence area (yellow in the animation above) which doesn't bring any benefit and it is not interesting. This is because the C point selected in the path are close to the Mandelbrot set.

[VittorioAccomazzi]

Fourth Attempt

Same as above, however selecting C values which diverge much faster. This allows to select the border od the mandelbrot set, and effectively generate Julia set which have less convergence points (yellow points). the result is that I find the fractal generated more interesting. Here is the path generated :

and here is a short video :

[VittorioAccomazzi]

I consider the fourth iteration satisfactory