Is it possible to animate the fake caustics using the lamp texture? I mean without moving the lamp so that it’s cyclic.
Yes, with the pointer/cursor in the lamp texture panel just use the “i” key to insert a key for locations and or size. You can the edit the ipo curves as with any other type of animation. I usually use several lamps overlapping each other repeating their animations in a different number of frames (I use prime numbers like 37). This way although the individual patterns repeat the effect as a whole doesn’t appear to repeat.
Also, how do you stop lamp textures from tiling
The same way as with other textures, in the panel where you load your texture their are extend, repeat, clip options. You may have to play with the dx, dy, dz and size buttons in the lamp texture panel to get it where you want.
Hope this helps