Structures in shapes: a perspective from rules and embedding

Jowers, Iestyn and Earl, Christopher (2017). Structures in shapes: a perspective from rules and embedding. In: Cultural DNA Workshop 2017, 13 Jan 2017, KAIST Graduate School of Culture Technology.

Abstract

Shape computations recognise parts and create new shapes through transformations. These elementary computations can be more than they seem, inducing complicated part structures as a result of recognising and transforming parts. This paper introduces, what is perhaps in principle, the simplest case where the part structure results from seeing embedded parts. It focusses on lines because, despite their visual simplicity, if a static representation for shapes is assumed, lines embedded in lines can give rise to more complicated structures than might be intuitively expected. With reference to the combinatorial structure of words the paper presents a thorough examination of these structures. It is shown that in the case of two lines, the resulting structure is always palindromic with parts defined by line segments of two different lengths. This result highlights the disparity between visual and symbolic computation when dealing with shapes – computations that are visually elementary are often symbolically complicated.