Miquel dynamics was introduced by Ramassamy as a discrete time evolution of square grid circle patterns on the torus. In each time step every second circle in the pattern is replaced with a new one by employing Miquel’s six circle theorem. Inspired by this dynamics we consider the local Miquel move, which changes the combinatorics and geometry of a circle pattern. We prove that the circle centers under Miquel dynamics are Clifford lattices, an integrable system considered by Konopelchenko and Schief. Clifford lattices have the combinatorics of an octahedral lattice, and every octahedron contains six intersection points of Clifford’s four circle configuration. The Clifford move replaces one of these circle intersection points with the opposite one. We establish a new connection between circle patterns and the dimer model: If the distances between circle centers are interpreted as edge weights, the Miquel move preserves probabilities in the sense of urban renewal.

拉马萨米（Ramassamy）引入了Miquel动力学，作为圆环上正方形网格圆圈图案的离散时间演变。在每个时间步中，通过使用Miquel的六圈定理，将图案中的第二个圆替换为一个新的圆。受此动力学启发，我们考虑了局部Miquel运动，该运动改变了圆形图案的组合和几何形状。我们证明了Miquel动力学下的圆心是Clifford格子，这是Konopelchenko和Schief考虑的可积系统。Clifford格具有八面体格的组合，每个八面体都包含Clifford四个圆构型的六个交点。Clifford的动作用相反的一个替换了这些圆的交点之一。我们在圆圈图案和二聚体模型之间建立了新的联系：