The objective of this pen-and-paper study is to monitor the growth of structural complexity as a function of the number of heavy atoms. This is done here using simple chloroalkanes, the indices of structural complexity being the number of regioisomers and mainly stereoisomeric features. Following a previous work dealing with acyclic alkanes, the present study focuses on all acyclic monochloroalkanes from four heavy atoms (four regioisomers) to 10 heavy atoms (2 to 211 regioisomers, respectively). Similarly, all acyclic dichloroalkanes were drawn, ranging from five heavy atoms to nine heavy atoms (4 to 130 regioisomers, respectively). The first part of the work describes the nature and number of stereoisomeric features seen to emerge in molecular structures featuring one or more stereogenic centers. These molecular features include enantiomerism, diastereoisomerism, pseudoasymmetry, and meso-isomerism. The first appearance of chirality among the monochloro and dichloro homologs occurred in the families with five heavy atoms. Diastereoisomerism, meso-isomerism, and pseudoasymmetry appear in higher families of homologs. The second part of the article is an attempt to rationalize the appearance of regioisomers, stereogenic centers, and stereoisomers as their number grows along homologous series, from one family of regioisomers to the higher ones. Far from being random as anticipated, such increases appear regular and ordered. Indeed, the data available demonstrate exponential increases and suggest the involvement of geometric order in the growth of chemical complexity.