Fractal Sequence applet

Upon starting up the Fractal Sequence applet, the user is presented with the following controls.

Fractal Sequence Applet (This is The Modified Chaos Game applet)

The ``Sample'' field defaults to $100,000$ points, so that the chaos game may draw a reasonably complete image before stopping to generate statistics. The user can edit this to any suitable nonzero natural number.

The ``addr. length'' defaults to $1$, which means that density statistics will be generated for addresses of length $1$. The user may make this any nonzero integer from $1$ to $6$. Once the specified number of points have been sampled, the programme pauses (about 20 seconds on my P160 laptop) to calculate densities, and then displays them in text format in ``Danny's data pit,'' as well as re-colouring the existing game points appropriately, before continuing to generate more game points.

The user can choose a ``Pattern'' -- an IFS with probabilities -- or construct their own. The probabilities in column ``p'' should sum to $1$.

At the bottom of the panel is a display of the number of game points generated, and a field where the user may indicate a substring to be filtered out (see Section 3). For no filtering, leave this field blank. There are two methods of filtering: the default is truncation (forbidden substrings have their last character removed) which is indicated by a ``T'' in the Method field. Users may also choose extraction by typing a capital ``X'' in the Method field -- forbidden substrings will be completely extracted.

Once these choices have been made, clicking the ``Fastest'' button begins plotting points, until ``Stop'' is clicked. Have fun.