Arbitrary precision

Ultra Fractal can perform fractal calculations with almost any desired precision. This enables you to zoom as deep as you want, without hitting a precision limit. This is called arbitrary precision or deep zooming.

Three types of precision are available:

• Double is the fastest and the least precise method. It supports magnifications up to about 10¹⁰ (1E10, or 10 billion). It has a precision of 15-16 decimals.
• Extended is slightly more precise and a little slower, supporting magnifications up to about 10¹⁶. It has a precision of 19-20 decimals.
• Arbitrary is much slower (but see Perturbation calculations), but it supports magnifications up to 10⁴⁰⁰⁰. Its precision can be scaled from 20 to 10,000 decimals.

Ultra Fractal automatically selects the best precision type, depending on the current magnification and the selected fractal formula, transformations, and coloring algorithms. It calculates the number of decimals required and selects the fastest precision type that can support it.

You can verify the number of decimals required and the selected precision type in the General tab of the Statistics tool window.

Sometimes, you may want to adjust the number of decimals to force Ultra Fractal to use a different precision type, or to change the number of decimals used with the Arbitrary precision type. The Additional Precision input box on the Formula tab of the Layer Properties tool window allows you to do this.

The value in the Additional Precision input box is added to the default number of decimals required. Positive values will increase the precision; negative values will decrease it. Keep an eye on the Statistics tool window to see the effect.

Notes

• It is not recommended to try and use the additional precision to achieve artistic effects, since they would rely on artefacts in the current implementation, and might be broken by future versions.
• Some older formulas rely on the Extended precision that was always used by Ultra Fractal 2. In this case, you can adjust the additional precision (looking at the Statistics tool window) until the Extended precision type is used.
• To force Ultra Fractal to always or never use Arbitrary precision, select the desired option in the Use arbitrary precision area on the Fractal tab of the Preferences dialog.

Next: Perturbation calculations

See Also
Fractal formulas