Infinite, almost any formula will do. Just try it:you give some formula which depends on some parameters and try with different random values, until you get a orbit that remains in the window producing an image.
Why not use directly the computer to discover new interesting formulas?
Is this the task of program ufattr that tries many different formulas keeping only those that give images in a window. In time a data base with around 50,000 formulas has been created. The search is continuing and the data base continues to grow.
Click here to look at the last found