In the applet above the white triangle corresponds to the set of all possible triangles, the blue "X" corresponds to the base triangle (i.e., the triangle the recursion starts with), this triangle is also shown on the left in yellow with angles indicated below. The red dots are the the triangles formed by using the indicated recursion method to the indicated depth.
By pushing the arrows you can change the recursion method to one of (bisectors, medians, Lemoine point, Gergonne point, Spieker center) and the depth to one of (1,2,3,4,5,6). You can also change the initial triangle by clicking or clicking and dragging inside the white triangle (dragging is recommended only for depth at most 4). The triangle shown on the right in orange (may take a few clicks to appear) corresponds to the triangle at your current cursor position.