Exponential interpolation

For floating point parameters, Ultra Fractal offers an additional interpolation setting called exponential interpolation. 

This can be set independently of the normal interpolation methods in the 

Timeline tool window

.

Exponential interpolation should be used for parameters that are exponential in nature. This means that in order to 

experience the same apparent increase of the parameter, you need to double it each time, instead of adding something.

A perfect example is the Magnification parameter on the Location tab. It starts at 1. If you add 1 to make it 2, the fractal 

is magnified by a factor of two. If you add 1 again, the fractal is magnified by only a factor of 1.5. If you keep adding 1, 

the apparent difference gets less and less. At a magnification of 1000, you will probably not notice it if you change the 

magnification to 1001. In contrast, if you keep multiplying the magnification with two, you will each time experience the 

same zoom effect. Clearly, the Magnification parameter is exponential in nature. In contrast, the Rotation Angle 

parameter is linear in nature.

This is important when interpolating animations, because exponential parameters must also be interpolated 

exponentially. For example, if you create an animation of 99 frames where Magnification ranges from 1 at frame 1 to 16 

at frame 99, it must be 4 at frame 50 to give the effect of a gradually increasing zooming level. With normal 

interpolation, it will be 8.5. Fortunately, the Magnification parameter uses exponential interpolation by default.

To turn exponential interpolation on and off for a parameter, open the Timeline tool window, select the parameter in the 

tree view, and click the Exponential interpolation check box.

Certain built in parameters in Ultra Fractal, such as Magnification, Stretch, and Color Density in the Inside and Outside 

tabs, are exponential by default. When you are writing a formula, you can also specify whether or not floating point 

parameters in your formula should be treated as exponential by default. See the 

exponential setting

.

See Also

Tutorial: Working with animations

Timeline

Interpolation

Animation

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