Mandala Symmetry
Symmetry describes how the basic snakes are replicated within the outer circle. A circle has 360 degrees. Symmetry divides the whole circle into pie-shaped wedges. The number of degrees in a wedge is computed by dividing 360 by the symmetry value. The following table summarizes the predefined symmetries.
Symmetry |
Wedge Angle |
Symmetry Description |
2-way |
180 | Reflection around the X-axis. |
| 3-way | 120 | Rotation through 120 degree intervals. |
| 4-way | 90 | Reflection around the X and Y-axis. |
| 5-way | 72 | Rotation through 72 degree intervals. |
| 6-way | 60 | Reflection and rotation. |
| 8-way | 45 | Reflection around the X-axis, Y-axis, and the 45 and 135 degree lines. |
| 9-way | 40 | Rotation through 40 degree intervals. |
| 10-way | 36 | Reflection and rotation. |
| 12-way | 30 | Reflection and rotation. |
All snakes live within a wedge that begins on the X-axis, and extends upwards, towards the Y-axis. Pixels in the remaining wedges are drawn by either reflecting or rotating pixels from the first wedge.
3-way, 5-way, and 9-way symmetry have an odd number of wedges. This implies that there cannot be a wedge directly across the circle from a given wedge. In these cases, the wedges are created purely by rotating the initial segment by the number of degrees in the wedge. The patterns produced by this technique tend to have a feeling of rotation or circular motion when viewed.
Last update: Monday, July 30, 2001 03:17:34 PM
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