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