Symmetry
Some fractal formulas always create images that are symmetric. Ultra Fractal can take advantage of the symmetry to speed up the calculation. To enable this, you must specify the symmetry of the formula as the optional setting between parentheses right after the entry identifier. Example:
Mandelbrot(XAXIS) { ... }
This formula is symmetric around the horizontal x-axis, therefore it uses the XAXIS setting. This table lists all possible values for the symmetry setting:
| XAXIS | Forces symmetry around the horizontal x-axis, or the real axis. |
| YAXIS | Forces symmetry around the vertical y-axis, or the imaginary axis. |
| XYAXIS | Forces symmetry around both the horizontal and the vertical axes. |
| ORIGIN | Forces rotational symmetry around the origin. This is useful for Julia sets. |
| PI | Not implemented. |
You can append _NOPARM to all values (thus obtaining XAXIS_NOPARM, etc) to make sure symmetry is only applied when all complex parameters are set to (0, 0). The XAXIS setting also allows the suffixes _NOREAL and _NOIMAG to disable symmetry for non-zero real and imaginary parts of all complex parameters.
Notes
- Symmetry is always disabled if the rotation angle set in the Location tab is not zero, or if a coloring algorithm that reads the value of #z is selected.
- It is not recommended and not reliable to use this to enforce symmetry that does not exist in the formula itself. It is only intended as a speed-up for formulas that naturally exhibit symmetry.
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See Also
Writing fractal formulas
Formula files and entries