We present Bharati, a simple, novel script that can represent the characters of a majority of contemporary Indian scripts. The shapes/motifs of Bharati characters are drawn from some of the simplest characters of existing Indian scripts. Bharati characters are designed such that they strictly reflect the underlying phonetic organization, thereby attributing to the script qualities of simplicity, familiarity, ease of acquisition and use. Thus, employing Bharati script as a common script for a majority of Indian languages can ameliorate several existing communication bottlenecks in India. We perform a complexity analysis of handwritten Bharati script and compare its complexity with that of nine major Indian scripts. The measures of complexity are derived from a theory of handwritten characters based on Catastrophe theory. Bharati script is shown to be simpler than the nine major Indian scripts in most measures of complexity. Self-organizing maps (SOM) are generated by training data for handwritten characters of Bharati and Indian scripts. Phonetically similar characters are clustered together on SOM for Bharati, supporting the proposition that the shapes of Bharati script follow the underlying phonetic organization. © 2017 IEEE.