A morphogenetic system (M system) is an abstract computational model inspired by characteristic properties of morphogenetic phenomena such as controlled growth, self-reproduction, homeostasis and self-healing in living systems. Besides selected principles of membrane computing, M systems also rely on algorithmic self-assembly of abstract tiles unfolding in a 3D (or generally, dD) space. Explicit spatial arrangements for interaction among an M system’s components are crucial for its function. From a computational viewpoint, key features of M systems include their computational universality and their efficiency to solve difficult problems. Both computational universality (in the Turing sense) and self-healing properties (in the sense of the algorithmic tile assembly model) have been demonstrated for different M systems in prior publications. Here, we demonstrate that both of these properties can be simultaneously achieved in a single M system. We present a Turing universal string acceptor M system that also exhibits self-healing capabilities of degree 1. This result is rather surprising since Turing machines are usually very sensitive to minor damage to their internal structure. The result thus sheds light on the power and importance of geometric and spatial arrangements for the reliability and robustness of a computational system.

形态发生系统（M system）是一种抽象的计算模型，其灵感来自形态发生现象的特征特性，例如生命系统中的受控生长、自我繁殖、稳态和自我修复。除了选定的膜计算原理外，M 系统还依赖于在 3D 中展开的抽象瓦片的算法自组装（或一般来说，dD) 空间。M 系统组件之间交互的显式空间安排对其功能至关重要。从计算的角度来看，M 系统的关键特征包括它们的计算通用性和解决难题的效率。在先前的出版物中，已经针对不同的 M 系统证明了计算通用性（在图灵意义上）和自愈特性（在算法瓦片组装模型的意义上）。在这里，我们证明了这两个特性可以在单个 M 系统中同时实现。我们提出了一个图灵通用字符串受体 M 系统，它也表现出 1 级的自愈能力。这个结果相当令人惊讶，因为图灵机通常对其内部结构的轻微损坏非常敏感。