Well, it seems (to me) that I have discovered a new Turtle-type fractal.

Here's a snapshot of the XLISP version:

The Brain fractal for n=12 iterations.

You can have the original XLISP sources [lost!] for MSDOS (unfortunatedly I was not able to compile it for LINUX) and the xlisp.exe binary (i.e. the LISP environment).
I have carefully checked it for viruses -- it seems to be clean.

Running it it's simple: unpack the archive to some directory and (from MSDOS or DOSEmu under Linux) type the following command:

xlisp brain.lsp

If you want to compile the binary by yourself, you can get the whole XLISP package.

I wanted to have a Java version of it.
Hence I have hardly worked on modifying the CLSFractal class from Sun's JDK.
After two days of hard programming I discovered that I did not have to modify the class itself but it was enough to modify the parameters for this class such that for a $n=12$ to have the same shape.
This is a paradoxical conclusion because the algorithm's primitives for moving the turtle are not the same. (You can convince yourself of that by running my LISP version with n running in {1,...,4} and the Java version for the same n)

You may compare the LISP version with the Java version