User:HighInBC/Fractal animation
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Fractal animation is the process of applying animation to a fractal. The parameters that are used to define what a fractal image will look like are iterated over and varied to create the illusion of change.
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[edit] Fractal Parameters
Different fractal formulas use different parameters, these are some that you would find in the Mandelbrot set. It is through the changing of these parameters that the appearance of change takes place, creating an animation. By using only parameters, a complex image can be created.
[edit] Real and imaginary
The real and imaginary parameters are often defined as x and y respectivly. By altering these parameters in a smooth fashion the appearance of movement occurs. It appears that your point of view is travelling along the fractal plane.
The real parameter is defined as a number between -2 and 1, and the imaginary parameter is defined as a number between 1 and -1 as shown to the left. Numbers outside those ranges can be supplied, but it will be outside the complex part of the mandelbrot and show little or no detail.
The manner in which these parameters are animated can be as simple as a straight line, or more complex methods such as using bezier curves or cardinal splines to plot a course using waypoints. These sorts of mathematical curves are often used in computer game development.
By using curves, a more fluid fealing of motion can be achieved, however this usually requires more work as most fractal animation software only allows you to plot straight lines.
[edit] Rotation
The rotation parameter changes the angle that the fractal is viewed from. This value is usually measured in degrees from 0 though 360(0 and 360 are considered equal).
Since fractals have infinite resolution, rotating a fractal image does not reduce quality as rotating a fixed precision image would do.
The direction of rotation in an animations can come from a variety of sources including facing direction of travel, facing a fixed point, facing a moving point, or manually plotted directions.
[edit] Color cycling
Some methods of coloring a fractal involve a series of colors laid out in a specific order. By cycling the position of these colors it appears that the colors drift. Color cycling does not change the shape or position of the image on the screen, only how is it colored.
