ABSTRACT
An exploratory study is performed on the dynamics of discrete maps in the complex plane endowed with memory of past iterations. This chapter deals with the generalized breakout condition that generates the so-called biomorphs, that is, a kind of Julia sets whose form resembles that of certain types of living microorganisms. It shows how embedding memory in the unaltered functions defining the kind of Julia sets generated in iterated complex maps with a non-canonical convergence criterion, that is, biomorphs, reveals an inexhaustive new reservoir of shapes and patterns. Combinations of algebraic and transcendental transformations are more likely to produce interesting results in the search for biomorphs. The effect of delay memory on biomorphs is not properly scrutinized here but it has been ascertained that, although as a general rule the effect of delay memory is qualitatively similar to that studied here according to, the details in the patterns may vary notably.
