An iterated function system (IFS) is a function or set of functions which operate on data repeatedly. Often, the input and/or functions are kept simple so as to be more easily analyzed. Some examples of IFS include the dragon fractal, Sierpinski triangle, Koch curve, L-systems and the Mandelbrot set. By way of example, below is the Sierpinski triangle followed by another similar fractal shown step by step (for three steps each):
```________________
|              |
| |_           |
|              |
|              |
|              |
|              |
|              |
|              |
----------------
________________________________
|              ||              |
| |_           || |_           |
|              ||              |
|              ||              |
|              ||              |
|              ||              |
|              ||              |
|              ||              |
--------------------------------

________
|      |
|      |
|      |
|      |
--------
________________
|      ||      |
|      ||      |
|      ||      |
|      ||      |
----------------
________        ________
|      |        |      |
|      |        |      |
|      |        |      |
|      |        |      |
--------        --------
________________________________
|      ||      ||      ||      |
|      ||      ||      ||      |
|      ||      ||      ||      |
|      ||      ||      ||      |
--------------------------------

____
|  |
|  |
----
________
|  ||  |
|  ||  |
--------
____    ____
|  |    |  |
|  |    |  |
----    ----
________________
|  ||  ||  ||  |
|  ||  ||  ||  |
----------------
____            ____
|  |            |  |
|  |            |  |
----            ----
________        ________
|  ||  |        |  ||  |
|  ||  |        |  ||  |
--------        --------
____    ____    ____    ____
|  |    |  |    |  |    |  |
|  |    |  |    |  |    |  |
----    ----    ----    ----
________________________________
|  ||  ||  ||  ||  ||  ||  ||  |
|  ||  ||  ||  ||  ||  ||  ||  |
--------------------------------
```

```________________
|            _ |
|           |  |
|              |
|              |
|              |
|              |
|              |
|              |
----------------
________________________________
|              ||              |
| |_           ||              |
|              ||              |
|              ||              |
|              ||              |
|              ||              |
|              || _|           |
|              ||              |
--------------------------------

________________
|      ||      |
|      ||      |
|      ||      |
|      ||      |
----------------
________
|      |
|      |
|      |
|      |
--------
________                ________
|      |                |      |
|      |                |      |
|      |                |      |
|      |                |      |
--------                --------
________________________________
|      ||      ||      ||      |
|      ||      ||      ||      |
|      ||      ||      ||      |
|      ||      ||      ||      |
--------------------------------

________________
|  ||  ||  ||  |
|  ||  ||  ||  |
----------------
____        ____
|  |        |  |
|  |        |  |
----        ----
____
|  |
|  |
----
________
|  ||  |
|  ||  |
--------
________                ________
|  ||  |                |  ||  |
|  ||  |                |  ||  |
--------                --------
____                        ____
|  |                        |  |
|  |                        |  |
----                        ----
____        ________        ____
|  |        |  ||  |        |  |
|  |        |  ||  |        |  |
----        --------        ----
________________________________
|  ||  ||  ||  ||  ||  ||  ||  |
|  ||  ||  ||  ||  ||  ||  ||  |
--------------------------------
```

With the three-way IFS above, many of the fractals that are produced are simple reflections or restatements of each other. Out of 512 possible fractals, only 200 or less are unique for this particular IFS form.
I worked in the extra spaces above to make sure that the overall idea is clear.