  In many complex dynamical systems, artificial or natural, one can observe
self-organization of patterns emerging from local rules. Cellular automata,
like the Game of Life (GOL), have been widely used as abstract models enabling
the study of various aspects of self-organization and morphogenesis, such as
the emergence of spatially localized patterns. However, findings of
self-organized patterns in such models have so far relied on manual tuning of
parameters and initial states, and on the human eye to identify interesting
patterns. In this paper, we formulate the problem of automated discovery of
diverse self-organized patterns in such high-dimensional complex dynamical
systems, as well as a framework for experimentation and evaluation. Using a
continuous GOL as a testbed, we show that recent intrinsically-motivated
machine learning algorithms (POP-IMGEPs), initially developed for learning of
inverse models in robotics, can be transposed and used in this novel
application area. These algorithms combine intrinsically-motivated goal
exploration and unsupervised learning of goal space representations. Goal space
representations describe the interesting features of patterns for which diverse
variations should be discovered. In particular, we compare various approaches
to define and learn goal space representations from the perspective of
discovering diverse spatially localized patterns. Moreover, we introduce an
extension of a state-of-the-art POP-IMGEP algorithm which incrementally learns
a goal representation using a deep auto-encoder, and the use of CPPN primitives
for generating initialization parameters. We show that it is more efficient
than several baselines and equally efficient as a system pre-trained on a
hand-made database of patterns identified by human experts.
