A Matter of 3-Dimensionality

The construction of the repeat unit (Figure 1) for this design was taken from page 79 of Geometric Concepts in Islamic Arts by Issam El-Said & Ayse Parman. This is an elegant method comprising of three concentric hexagonal stars (these are coloured blue in the animation. The red lines are for the construction and only the black lines of the unit are carried forward).
When the unit is repeatedly copied to a hexagonal grid (Figure 2) a new component emerges. This can be seen as three arrows radiating from a central point 120 degrees apart. In this form the arrows can be interpreted as the x,y and z coordinates of a spatial grid. The 3-dimensionality of this pattern can be further exposed by the addition of colour. Figure 3 is partially rendered to illustrate this.
Figure 4 shows the completed design which not only highlights the 3-D effect but displays the properties of an optical illusion - units in the pattern can be seen as building outwards or as cutting in. Either way, this can be interpreted as a rudimentary stalactite ceiling and I am now of the opinion that since this sort of design can plainly be constructed, they were fundamental to the process that led to the inspiration for those glorious ceilings that we see now.

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