04952nam a22006855i 4500 978-3-031-44821-8 DE-He213 20251030111428.0 cr nn 008mamaa 240216s2024 sz | s |||| 0|eng d 9783031448218 978-3-031-44821-8 10.1007/978-3-031-44821-8 doi TA352-356 QC20.7.N6 TBJ bicssc GPFC bicssc SCI064000 bisacsh TBJ thema GPFC thema Mowitz, Joachim H. author. aut http://id.loc.gov/vocabulary/relators/aut 71092 Movements of Form [electronic resource] / by Joachim H. Mowitz, Arno L. Goudsmit. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XV, 107 p. 82 illus., 77 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Vision, Illusion and Perception, 2365-7480 ; 6 Introductory remarks -- A self-referential boundary -- Expanding forms: the geometrical representation -- The geometrical expansions as a relational network -- The geometrical representation and its computability -- Conclusion -- References. This book offers a thought-provoking exploration of dynamic geometry and its connections to self-reference and theoretical biology. The authors explore how a self-referential boundary can be translated into remarkable relations between expanding geometrical forms, with a particular focus on triangles and circles. The essence of this work lies in revealing not only how these forms expand and interact with others but also how their interactions lead to closed loops of definitions between processes, where triangles and circles reciprocally define one another. These unique geometrical relations offer fresh perspectives on the interaction and emergence of forms. Through the introduction of time and a fixed velocity of expansions, a rich tapestry of encounters and coalescences unfolds, pushing beyond the boundaries of traditional insights on context dependence and state transitions of systems. These captivating movements elude prediction other than by numerical approximation within unpredictable durations. Unlike cellular automata, they defy stepwise progression on a predefined grid, presenting themselves as unprogrammable construction processes that leave readers in awe of their unexpected elegance. This book is essential reading for researchers and students in theoretical biology seeking to deepen their understanding of the intersections of geometry and systems theory and seeking to gain new insights into the processes that underlie the origination of complexity. "What is unique to the authors' attempt is to shed a new light on extending the notion of cohesive interaction so as to make it applicable even to biology at large without offending the established physics so far. To the best of my knowledge, their work has been the first attempt of this kind in explicating the intricate relationship between geometric topology of the network and the realizable temporal cohesion to be observed widely in biology." (Professor Koichiro Matsuno, 1st foreword to this book) "I am delighted that the authors use Robert Rosen's (M,R)-systems — impredicative networks that are inherently geometrical — to illustrate (see Chapter 4 of this book) their self-referential systems of geometrical expansions." (dr. Aloisius Louie, 2nd foreword to this book). Dynamics. 65524 Nonlinear theories. 65525 Engineering mathematics. 64145 Engineering Data processing. System theory. 66519 Graphic arts. 67280 Arts. 65405 Control engineering. Applied Dynamical Systems. 65530 Mathematical and Computational Engineering Applications. Complex Systems. 66520 Graphic Design. 67281 Arts. 65405 Control and Systems Theory. 65868 Goudsmit, Arno L. author. aut http://id.loc.gov/vocabulary/relators/aut 71093 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031448201 Printed edition: 9783031448225 Printed edition: 9783031448232 Vision, Illusion and Perception, 2365-7480 ; 6 71094 https://doi.org/10.1007/978-3-031-44821-8 ZDB-2-ENG ZDB-2-SXE 57659 57659