Narrow Results

We propose a method of description and modeling of complex symmetrical images, which can be used for the synthesis of ornamental patterns. Our approach allows considerable memory reduction for storing symmetrical images and considerable time reduction for their synthesis. Our algorithms for ornamental patterns synthesis suggest the design of a special purpose ornamental patterns editor which can store and synthesize symmetrical images.

We use a triple-point version of the Whitney trick to show that ornaments of three orientable $(2k-1)$-manifolds in ${ℝ}^{3k-1}$, $k>2$, are classified by the $\mu$-invariant.

A very similar (but not identical) construction was found independently by I. Mabillard and U. Wagner, who also made it work in a much more general situation and obtained impressive applications. The present note is, by contrast, focused on a minimal working case of the construction.