@Markiyan Hirnyk I am obtaining some understanding of this matter from the textbook that the OP is using: Modern Computer Algebra by Joachim von zur Gathen and Jurgen Gerhard. If you can access this book, I direct your attention to section 14.6 "Squarefree factorization". Some relevant quotes:

We will show how to reduce the problem of factoring arbitrary polynomials to that of factoring squarefree polynomials. Polynomial factorization software usually performs this reduction first; it is not quite clear when the (small) advantage one gains outweighs the (small) cost of the reduction.

And

The squarefree decomposition provides more information than the squarefree part. For a nonconstant monic polynomial f \in F[x], this is the unique sequence of monic squarefree pairwise coprime polynomials (g[1], ..., g[m]) with f = product(g[k]^k, k= 1..m) and g[m] <> 1. For example, the squarefree decomposition of x^4*(x+1)^2*(x-1)^2*(x^2+1)^2*(x^2+x+1) \in Q[x] is (x^2+x+1, x^4-1, 1, x). Thus g[i] is the product of those monic irreducible polynomials that divide f exactly i times.

@Axel Vogt Your files did not attach properly. This is a bug in MaplePrimes.

@Adri van der Meer 

For me, on Windows, currentdir() returns the currently active directory, but it doesn't return the directory of the current worksheet.

@candy898 So you are in fact using the book Modern Computer Algebra by Joachim von zur Gathen and Jurgen Gerhard. Why didn't you say so?

@Markiyan Hirnyk Here's an example where sqrfree and factor give different results:

f:= expand((x^2+x+1)*(x^3+x^2+x+1));
sqrfree(f);
factor(f);

@Markiyan Hirnyk No. If I could base them, I wouldn't have used the words "perhaps" and "suspect."

@Markiyan Hirnyk Good question. There is no difference in these cases, nor do I know of a case where there is a difference. There is perhaps a difference for some complicated polynomials. By the definition, the given factors need not be irreducible, they simply are forbidden to have repeated factors. There is an analogous situation with isqrfree and ifactors. I suspect that the reason that these commands exist is that the square-free factorization is much easier to compute than the full factorization.

@sm3scott If you use " ", then you have quotes within quotes. Try using backquotes instead: ` `.

Your file did not attach correctly. Please try uploading again. You can also try cut-and-pasting your code directly in a Reply.

@Preben Alsholm It is amazing/sad how many different attempts were made at this problem without Maple giving any hint that there was a syntax error. The OP even thought that he was making progress towards a solution/fit.

@acer It is not clear to me whether the intended operation was `*` or `/`, but clearly some operator is needed.

@brian bovril The benefit of using an iterator, such as from the Iterator package, is that you can quit before you've generated all the partitions.

@J F Ogilvie What exactly did you have to do to get it to work? It would be nice to get you a higher-resolution graphic. What operating system are you using? Maybe changing jpeg to jpg would help.

Feel free to use the code and graphic, but please mention my name.

Note that the CodeTools:-Usage is just to print the timing and memory info. You can also get rid of the caption and maybe the axes.

Also check out this very simple fractal that I posted on New Year's Day 2013.

@J F Ogilvie The only thing I can think of is that the plotoptions is not working on your computer. You changed the file name for the output, right? Try removing the plotoptions line from the plotsetup command. If that doesn't work, then remove the entire plotsetup command (and do a restart) to see the plot inline and reduce the grid to [400, 400] or less (and be prepared to wait for the plot to render on your screen).

Let me know how that goes.

@brian bovril Since the minimum variation is about 38, you'll need to set your cut-off much higher than 0.021.