Smart high school girls

On our schoolyard consists of large square pavement tiles. They collectively form a pattern that is the same as the graph paper that the students use for their mathematics assignments.

This year, the girls have a riddle for you. They mark a mathematical figure on the tiles of the schoolyard and you should figure out what figure that is.

Here is a description:
First the six girls place themselves on one stone, a little tight, but okay. Then they agree on the number of tiles they will walk in a specicic direction. Two girls go north, two east and two west. Then they turn towards the direction they came from. So, two girls still share the same tile. Now they remember: LOW = –1, HIGH = twice the mumber of tiles and FLAG = the number of tiles minus 1.

They put a cross on each tile on which they arrive, starting with the tile they are now standing on. Now Alice, Cindy and Emily will always step one tile to the left and Belinda, Daisy and Florence will always step one tile to the right. Whether or not they take a step forward at the same time depends on the outcome of a calculation they make. As soon as the girls hit the same tile the figure is ready.

Starting position and the two possible steps for Daphne.

The calculation at every step is: LOW is decreased by 2; FLAG is increased by LOW. If FLAG is smaller than LOW the girls take a step aside also and a step forward and they do an extra calculation: HIGH is increased by 2 and then HIGH is added to FLAG. In all other cases the only step aside.

Do you already know which mathematical figure is drawn on the schoolyard? If not, play the simulation or read the answer at the bottom of this page.

Recently two of the girls have a boyfriend. For this time I have let these boys participate. In the simulation they use a green chalk.
Hint: Do not choose too little tiles.
Play the simulation now.   This simulation will work well if the screen has at least 900 pixels horizontally. If not, you get a warning, but will be able to play. Maximize your browser or use Ctr - – or Ctr - mouse wheel to get a smaller font. 

The girls mark three-quarters of a circle.