Morphogenetic computing is a fundamentally new approach to computing that attempts to add consistency and stability in uncertain situations. Valued logic or machine learning may be applied to reason in uncertain situations. However, these approaches are not 100 percent consistent. Their generalization capabilities are bought with fuzziness.

Morphogenetic computing might be placed in the field of natural computation, since the morphology of the modeled system may change over time, and this is comparable to evolving solutions in evolutionary and genetic algorithms. However, a difference is that in evolutionary search or in any other natural computing approach, problems are solved recursively. The authors’ techniques solve problems with purely algebraic methods. In feed-forward artificial neural networks (ANNs), backpropagation was one of the first successful training algorithms for nonlinear function approximation; despite its weaknesses, it still is. In the introduced approach, instead of propagating the error backwards through the network, the desired output vectors are, one by one, projected into the vector space of the input vectors by a projection operator, for which the linear combination of the column vectors assumes the difference between the projection of the outputs in the input space and the target vectors. Sometimes, the distinction between what the authors classify as morphogenetic computing is not 100 percent clear. For example, although one of the properties of morphogenetic computing in ANN training is that it is non-recursive, on another occasion it is defined as approaching leveraging recursion with invariance. In summary, the book describes combinations of algebraic methods for making global and local relations more stable and efficient. Examples problems include defects in crystals, non-Euclidean geometry, databases with source and sink, genetic algorithms, and neural networks.

Morphogenetic computing, as introduced here, is not one specific method for solving a variety of problems, but is a way of combining a variety of methods, mostly from vector algebra, to solve particular problems. The book covers the background in databases, graph theory, and linear algebra that is needed to understand morphogenetic computing. The authors use practical examples to explain concepts and their ideas.

An example given for a non-coherent situation is mapping an ideal network “in crystal with curvature [resulting in] incoherence in a loop similar to the sphere incoherence for vectors.” That, in turn, can be interpreted as a line defect in a crystal structure, which violates rotational symmetry. Given a point in this structure, the very same point can, in a loop, be “split into two parts, one for the source and the other for the sink,” which is called “dislocation because the same entity or point is dislocated in two different parts.”

For machine learning applications, the authors explain how to use morphogenetic computing with genetic algorithms and neural networks. They use a morphogenetic feedback loop, which considers input vectors, target values, and rules, and uses a projection operator that changes the external vectors with external rules to the internal vectors with rules given by samples. This is not the same as the feedback loop used in normal backpropagation. The authors also show that their computing paradigm can be used for physical systems, for example, electrical circuits.

The book is intended for people with intermediate knowledge of database and graph theory, as well as some basic knowledge in machine learning. Although the authors cover all required mathematical concepts to understand morphogenetic computing, the explanations are sometimes cumbersome. Furthermore, the reader will notice that the book was not written by native English speakers and would have benefited from further proofreading.