Seeded Examples

Seeded Form Examples

These Seeded Form Examples display various types of symmetries and hint at the extremely high number of potential seeded forms. (See Muqarnas / Mogharnas presentation.)

The 3D view of each of the sixteen (16) mogharnas tiles I use in my creations can be seen here.

1-3-1-3-1-7 X2 Seed

The 1-3-1-3-1-7 X2 Seed displays symmetry in two planes at right angles. Each tile is 180° opposite an identical tile. Thus, any set of contiguous tiles totaling 180° is matched by an equal and opposite set. So this type of seed is [(set) X2]. Since I chose to use the muqarnas tiles which use 32-fold symmetry there are other possible symmetries which have multiple groups of elements. In addition to X2, X4, X8, X16, X32.

Seeded mogharnas symmetry can be chiral or non-chiral. Thus, the chiral Crescent motif could be used for form expansion. This example has the central dome expanded with three tiers using the Ray motif.

One (1) times 11.25° = 11.25°

Three (3) times 11.25° = 33.75°

Seven (7) times 11.25° = 78.75°

1-3-1-3-1-7 X2 Four Views

1-3-1-3-1-7 X2 Seed

1-3-1-3-1-7 X2 Seed and Form

This form uses the seed expanded to three additional tiers with the Ray motif. The Ray motif provides the simplest and most reliable method for expanding mogharnas / muqarnas forms, which is why I use it so often.

1-3-1-3-1-7 X2

1-3-5-3-8-3-5-3-1 Seed

One (1) times 11.25° = 11.25°

Three (3) times 11.25° = 33.75°

Five (5) times 11.25° = 56.25°

Eight (8) times 11.25° = 90.00°

The 1-3-5-3-8-3-5-3-1 Seed displays mirror symmetry. So the 1-3-5-3 tiles are in the mirror image position of the 3-5-3-1 tiles. The 8 tile is dissected by the mirror plane and, thus, is self-mirrored. This form has the central dome expanded with two tiers using the Ray motif.

1-3-5-3-8-3-5-3-1 Four Views

1-3-5-3-8-3-5-3-1 Seed

2-1-3-1-5-2-3-3-2-5-1-3-1 Seed

One (1) times 11.25° = 11.25°

Two (2) times 11.25° = 22.5°

Three (3) times 11.25° = 33.75°

Five (5) times 11.25° = 56.25°

Like the previous seed, the 2-1-3-1-5-2-3-3-2-5-1-3-1 Seed also displays mirror symmetry. The 1-3-1-5-2-3 tiles are in the mirror image position of the 3-2-5-1-3-1 tiles. The non-paired 2 tile is dissected by the mirror plane and, thus, is self-mirrored. This form has the central dome expanded with two tiers using the Ray motif.