To test this idea I define a simple computing machine, a kind of calculator. This machine has a accumulator, a stack and can execute only the set of 22 commands reported in table 1. I generate a random fractal by creating two random sequences of commands for this machine,one to compute the new value of x, the other for y. This is the algorithm which is repeatedly executed starting with some arbitrary (x0,y0) and then feeding back the previous result at each iteration. By repeating this procedure for all (x0,y0) in some range a<x0,y0<b than representing in color the number of times necessary for the accumulator to go to infinity, I can create an image:the Julia set of the formula. Figure 1 shows those sets for 196 different formulas generated randomly by the program reported in Appendix 1 implementing the set of commands given in table 1. I have called this program "ufmac" since it attempts to be a kind of "universal fractal machine". In the C code reported here the number of commands for the x and y parts are stored in array "nsel". The array "isel" contains the opcodes and array "c" the constants for the algorithm generated. For example the formula (1) would correspond to the following values of nsel,isel and c:
int nsel[2] = { 6, 4};
int isel [2] [50] = { { 14, 8, 16, 7, 20, 3},
{ 14, 7, 9, 3}};
float c [2] [50] = {{0.,0.,0.,0.,0.,.53},
{0.,0.,2.,.32}};