Kiora, I'm Nanako and this is Strea. In this work, we theoretically explored the geometrical statistical properties of the spindermains that form an equate spinner Bose-Einstein condensate. A spinner Bose-Einstein condensate is an ultra-code guess of bosonic ashams in which each ash has access to several different spin states. In our case, we study a spin-1 system with three accessible spin levels. The ashams in the condensate we consider also have theorem-ethetic interactions, which means that these interactions favor the system magnetizing. We consider the system prepared in an initial state that is un magnetized. The quenches implemented by suddenly changing the quadratic Z-men energy to a value at which this condensate is unstable, so that it forms easy access magnetic domains. That is, spin domains that are aligned with or against the direction set by the Z-men field. In this simulation, we show the dynamics of a small, quasi-two-dimensional condensate undergoing this evolution. Starting from the un magnetized state, you will notice a small domains form. Then, as time progresses, these domains tend to grow larger. We analyze the structure of these domains once they form. To do this, we have applied the ideas of percolation theory. Notably, we focus our attention on the positive or upward pointing spin domains. We can make a binary image by setting all positive domains to be white. We examine if any of these domains percolate across the system. Here is an example of percolating domain that connects from the lower boundary to the top boundary. This domain also happens to connect the left and right boundaries. In order to explore percolation characteristics, we need to change the relative portion of atoms in the positive domain and see how this affects the probability of a percolating domain occurring. In this work, we varied the positive domain populations using a coherent spin rotation, a standard technique of atomic physics experimental to a box. We find that the probability of finding a percolating domain varies smoothly as a portion of positive atoms is varied. Thus, identifying a smooth percolation transition. Conducting a finite size analysis, we examine how this probability changes as the system size increases. This allows us to extrapolate to the thermodynamic limit, where the transition is discontinuous, and hence identify the percolation threshold and the correlation length critical exponent. In addition to showing that spin domain formation can be described by percolation theory, we also examine the feasibility of studying this behavior in experiments. That is, we examine factors such as the time dependence of domain growth and the continuous nature of the spin density on the percolation analysis. We also suggest a way to minimise heating from the quench by its preparing a sociable initial stage. We hope that this work will inspire experiments to make the first studies of percolation in an ultra-called atomic gas.