Scott, Could I ask you why you use extra local variables in your code, such as,

// create container layer for spheres
CALayer* sphereContainer = [CALayer layer];
sphereContainer.name = @"sphereContainer";
[mainLayer addSublayer:sphereContainer];
self.containerLayerForSpheres = sphereContainer;

As opposed to,

// create container layer for spheres
self.containerLayerForSpheres = [CALayer layer];
self.containerLayerForSpheres.name = @"sphereContainer";
[mainLayer addSublayer:self.containerLayerForSpheres];

You perform a similar action with sphereCount as well. I'm learning Cocoa and would love to know if the second form is significantly less efficient or if there is some other possible problem. Cheers!