# Maximum iterations

To calculate a pixel in a fractal, Ultra Fractal iterates the selected fractal formula. It executes it multiple times, each time using the result from the previous calculation as input.

The formula is iterated until the maximum iteration count is reached, or until the bail-out condition (specified by the fractal formula) is met. If the bail-out condition is met, the pixel is colored as an outside pixel. Otherwise, it is colored as an inside pixel.

Sometimes, many iterations are necessary to reach the point where the bail-out condition is satisfied. If the maximum iteration count is too small, the pixel will be incorrectly colored as an inside pixel because the bail-out point is not reached. On the other hand, if the iteration count is too large, many iterations will be performed for the pixels that are inside, and the fractal will be calculated slowly.

The Maximum Iterations setting on the Formula tab of the Layer Properties tool window specifies the maximum iteration count. To help you find a good value, the Statistics tool window shows a histogram of the iteration values on its Iterations tab.

This example illustrates the influence of the maximum iterations setting:

 Maximum iterations: 20 Maximum iterations: 200 Maximum iterations: 2000

We see the same image three times, with three different values for the maximum number of iterations. Below each image, the iterations histogram from the Statistics tool window is shown.

The first image clearly suffers from a low value for the maximum iterations setting. By increasing it, we obtain the second image, which looks much better. Further increasing the value does not change the image much, so we conclude that 200 is a good value in this case.

Notes

• The histogram can aid you in deciding whether or not you have to change the maximum iterations value. If most of the iterations end up on the left side (as with the middle image), you are probably safe. If they are all at the far left side, the value is probably too high (which makes the fractal slower to calculate). If there are many iterations on the right side, the value is too low. Move the mouse pointer over the tool window to see the corresponding iteration values.
• Experiment with the maximum iterations setting to learn how to use it. Sometimes, a (too) low value can also be artistically pleasing.
• By checking the Adjust Automatically checkbox on the Formula tab, Ultra Fractal automatically adjusts the maximum iterations value when zooming in or out. This can be helpful, but it is not fool-proof: you may need to adjust the value manually every once in a while.

Next: Formula parameters