Are Julia and Mandelbrot sets the only types of fractals using complex numbers?
No. Don’t forget that by using polynomials of higher degree, with various number of terms and having coefficients of various values, you can have a great variety of Mandelbrot-like and Julia-like sets. Moreover, the iterations of almost all formulas using complex numbers (in no way related to Julia or Mandelbrot formulas) lead to fractal structures. Fractal programs (with the exception of the simplest) have built in formulas, but also enable the user to enter his own formulas. The part of the program which runs user’s formulas is generally named the parser: it interprets (in the case of Ultra Fractal, it compiles) the formula and executes it. With the introduction of conditional loops in the characteristics of the parser, formulas may now be quite complex and are often indeed short programs on their own. If you are not a mathematician, you can freely use thousands of formulas which have been published.
