Active Self-Assembly of Algorithmic Shapes and Patterns in Polylogarithmic Time

We describe a computational model for studying the complexity of self-assembled structures with active molecular components. Our model captures notions of growth and movement ubiquitous in biological systems. The model is inspired by biology's fantastic ability to assemble biomolecules that form systems with complicated structure and dynamics, from molecular motors that walk on rigid tracks and proteins that dynamically alter the structure of the cell during mitosis, to embryonic development where large-scale complicated organisms efficiently grow from a single cell. Using this active self-assembly model, we show how to efficiently self-assemble shapes and patterns from simple monomers. For example, we show how to grow a line of monomers in time and number of monomer states that is merely logarithmic in the length of the line. Our main results show how to grow arbitrary connected two-dimensional geometric shapes and patterns in expected time that is polylogarithmic in the size of the shape, plus roughly the time required to run a Turing machine deciding whether or not a given pixel is in the shape. We do this while keeping the number of monomer types logarithmic in shape size, plus those monomers required by the Kolmogorov complexity of the shape or pattern. This work thus highlights the efficiency advantages of active self-assembly over passive self-assembly and motivates experimental effort to construct general-purpose active molecular self-assembly systems

Margarita de Sossa, Sixteenth-Century Puebla de los Ángeles, New Spain (Mexico)

Margarita de Sossa’s freedom journey was defiant and entrepreneurial. In her early twenties, still enslaved in Portugal, she took possession of her body; after refusing to endure her owner’s sexual demands, he sold her, and she was transported to Mexico. There, she purchased her freedom with money earned as a healer and then conducted an enviable business as an innkeeper. Sossa’s biography provides striking insights into how she conceptualized freedom in terms that included – but was not limited to – legal manumission. Her transatlantic biography offers a rare insight into the life of a free black woman (and former slave) in late sixteenth-century Puebla, who sought to establish various degrees of freedom for herself. Whether she was refusing to acquiesce to an abusive owner, embracing entrepreneurship, marrying, purchasing her own slave property, or later using the courts to petition for divorce. Sossa continued to advocate on her own behalf. Her biography shows that obtaining legal manumission was not always equivalent to independence and autonomy, particularly if married to an abusive husband, or if financial successes inspired the envy of neighbors

Active Self-Assembly of Algorithmic Shapes and Patterns in Polylogarithmic Time

We describe a computational model for studying the complexity of self-assembled structures with active molecular components. Our model captures notions of growth and movement ubiquitous in biological systems. The model is inspired by biology's fantastic ability to assemble biomolecules that form systems with complicated structure and dynamics, from molecular motors that walk on rigid tracks and proteins that dynamically alter the structure of the cell during mitosis, to embryonic development where large-scale complicated organisms efficiently grow from a single cell. Using this active self-assembly model, we show how to efficiently self-assemble shapes and patterns from simple monomers. For example, we show how to grow a line of monomers in time and number of monomer states that is merely logarithmic in the length of the line. Our main results show how to grow arbitrary connected two-dimensional geometric shapes and patterns in expected time that is polylogarithmic in the size of the shape, plus roughly the time required to run a Turing machine deciding whether or not a given pixel is in the shape. We do this while keeping the number of monomer types logarithmic in shape size, plus those monomers required by the Kolmogorov complexity of the shape or pattern. This work thus highlights the efficiency advantages of active self-assembly over passive self-assembly and motivates experimental effort to construct general-purpose active molecular self-assembly systems