Is there any limit to the complexity of objects that an abiotic process can construct in abundance? This question is of importance to biosignature science, but a central challenge has been finding a physically meaningful measure of complexity that can be measured in the lab. Recently, the Assembly Index defined as the smallest number of recursive joining steps to assemble an object, has been shown to be experimentally measurable for molecules. The assembly index along with copy number of objects form the foundations of observables in Assembly Theory [Sharma et al, 2023], which aims to quantify how much selection was necessary to generate a given configuration of objects. Applied to life detection, assembly theory was empirically demonstrated to distinguish chemical products derived from biological and abiotic samples [Marshall, et al. 2021]. Though the empirical results seem to place an upper bound on abiotic complexity, it is not yet possible to generalize from these measurements to environments beyond Earth without an explanatory model. Here we present an approach for calculating an object’s assembly path length distribution, where an assembly path refers to a minimal sequence of assembly steps which build an object, and the expected path length is the mean of the distribution. We show, in the absence of any constraints, the expected path length scales exponentially with the assembly index. This allows us to describe the existence of two scaling regimes, one where expected path length scales exponentially with assembly index, and with sufficient constraints to lead to a linear scaling. An abrupt transition between the two regimes would be indicative of a selection-mediated phase transition.

Logic gates form the basis of modern digital computers, and from a theoretical perspective they are the unit of computation since they are the fundamental discrete logic element. By creating circuits of interconnected logic gates, computers can calculate more complex operations, such as adders, multiplexers, flips-flops, and eventually processing and control units. Herein, we use a 3D-printed platform consisting of a rectangular 2D-array of interconnected cells containing the Belousov–Zhabotinsky (BZ) reaction. This reaction can be made to oscillate between two states to simulate the binary codification of digital electronics. Within the platform each cell contains a magnetic stirrer that can be individually stirred to control the local oscillations of the BZ reaction in that cell, but all the cells are also weakly interconnected through the common medium, and here we used the convolution of their individual oscillations to perform heterotic computations. Moreover, the 3D-printed vessel can be fabricated using different architectures, to for example define how the cells are connected, and thus controlling how the oscillations propagate between them. We took advantage of these features to simulate the ”AND”, ”OR, and ”XOR” logic gates. We also implemented a 2D Cellular Automata. To do so we defined the cells where the BZ reaction oscillates as “on”, and set the transition rule as the propagation of oscillations from the “on” cells towards “off” ones. These results pave the way towards the development of more sophisticated unconventional computers, which might potentially enhance future Artificial Life implementations more effectively than current silicon-based advancements.

One of the salient features of living systems is presence of autocatalytic chemical reaction networks. Here we present a stochastic model of an inorganic autocatalyst, which is derived directly from empirical results. Using the model, we can explore the emergence of autocatalysis and its consequences on the larger, hierarchical, chemical network. This model provides a useful tool to study the emergence and organization of autocatalytic chemical networks and the effect autocatalysis has on the global system dynamics.