When an earthquake hits, a building or a tower might fall over if it starts shaking back and forth in sync with the earthquake.

For earthquake resistance, parts of the tower should absorb the vibration from the earthquake without causing the entire tower to rock back and forth. One way to do this would be to connect pieces of your tower with "wiggle-room" so that if one part of the tower moves, the other parts are not very rigidly attached and don't all move in unison. You could do this by putting something that will stay spongy (like a sponge!) between parts of your tower. In real buildings, these are components called "dampers" that absorb the vibration from the earthquake without having the whole building move.

Of course you also want to make sure that parts of your tower remain attached to each other if the vibrations cause bits of the tower to come apart. The sponge or gooey-glue connection between tower parts will help you here too: if the tower parts come apart a bit, the glue will still hold everything in place.

Finally, you want to make sure that your tower doesn't like to move in sync with the earthquake. You can't know what type of earthquake will hit, so it is best to just make sure that different parts of your tower have different weight and different thickness supports. That way, there wont be any earthquake that will match up with your whole tower.

Structures that are rigid tend to be brittle, while structures that are flexible have a difficult time standing up in the first place. Generally, a flexible network of cables surrounding rigid crystalline supports works best. Wood is made of such a mixture, which is why wooden structures are very strong for their weight, but steel is generally used for larger buildings because wood in trees has other functions as well that lessens its usefulness as a structural material (wood is mostly hollow so that water can flow through it).