In the beginning of Spacial Visualizer’s code, the vanishing point of the grid is initially set at the center of the canvas. As the mouse moves, the vanishing point dynamically changes based on the mouse's x and y coordinates. The function drawPerspectiveGrid then draws a grid with horizontal lines and vertical lines converging towards the updated vanishing point. The result is an interactive 3D perspective grid that adapts to mouse input, providing a visual demonstration of unique and unearthly perspective drawing principles.