
ALT Visualization of defect-driven chaos from a numerical simulation of a binary flocking mixture with nonreciprocal interaction from the paper “Breakdown of Emergent Chiral Order and Defect Chaos in Nonreciprocal Flocks.” Swirling patterns of deep red and blue against a white background show sweeping, wave-like and cloud-like textures of different scales resembling turbulent fluid motion.

ALT Four red, blue, and black particle density snapshots from the paper, “Extensive Spatiotemporal Chaos in Nonreciprocal Flocking.” Ordered from upper left to lower right, the snapshots show chiral order breaking down through spiral-shaped defects into a chaotic state in a nonreciprocal flock. As chiral order breaks down, large, sweeping patterns start to form until they dominate the entire snapshot.

ALT A depiction of the hierarchical symmetry engineering method described in this study. On the left is a ladder labelled symmetry ladder, with SU(2) in red on the top rung, U(1) in orange in the middle, and Z2 in green towards the bottom. To the left of the ladder are two squiggly arrows pointing at the ladder and on one of the ladder’s legs is a downward arrow that points to the word Time at the bottom. To the right is a graph depicting this same concept: the top is labelled prethermalization, the x axis is time and the y axis is order parameter. Lines of the same colors as the text on the ladder are used to draw inverted S curves, with SU(2) in red farthest to the left, followed by U(1) in orange, Z2 in green, and at the far right a curve in black labeled energy.

ALT Two beige circles against a black background represent how adding an extra qubit can double a quantum system’s maximum complexity. The left big circle shows this concept as a standalone. The right big circle shows how a state of maximum complexity turns into uncomplexity. Inside each circle are small blue circles and one large hollow peach circle. This image is from the original paper by Brown and Susskind that defined the second law of quantum complexity.

ALT Figure showing two self-assembly systems. On the left is a rigid body subunit shaped like a pentagon and a diagram showing the interactions that allow it to form a dodecahedron. Below are snapshots of the simulation box early and late in the process. The left one has many semi-formed subunits and structures. The right one has mostly dodecahedrons with a few subunits. On the right is a subunit with a rigid triangular body that forms a capsid. Below are snapshots of the simulation box early and late in the process. The left one has many small blue triangles. The right one has several fully-formed capsids and a few subunits.



















