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.
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.
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.
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.
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