Can you determine the first ten digits of the address of the point indicated by the marker? The names of the transformations are shown below the figure.
Scoring: Enter up to ten digits, each either $0,1,2$, with no spaces or other characters for your answer and click Mark. If the first digit of your answer is correct, you will earn 1000 points. Each consecutive correct digit after that is worth twice the preceding digit. Requesting a Hint cuts your score in half. Each attempt after the first also cuts your score in half. A perfect score is just over a million points. How high can you get?
The figure is the attractor of a HeeBGB IFS (see the Lecture Notes for Math 320 for details). If $S$ is the figure, and $S_0$, $S_1$, and $S_2$ are the three copies (which are always congruent to each other and similar to the original), then each copy determines a unique affine map $w_0$, $w_1$, and $w_2$, respectively, such that $$S=w_0(S)\cup w_1(S)\cup w_2(S)$$ Furthermore, $S$ is the unique closed bounded figure that satisfies that equation. All of the points in $w_{a_1}(w_{a_2}(w_{a_3}(\cdots w_{a_m}(S)\cdots)))$ have an address starting with $a_1a_2a_3\cdots a_m$.