Exercise: Finding order in chaos
Part 2. Viewing calculation paths
But it doesn't stop there. Do the following:
1) While holding down both the CTRL and SHIFT keys, click the bulb with three arms. This displays the calc path.
If the CTRL+SHIFT-click action does not display the calc path, check the left mouse button settings in the Left Button page of the Preferences window.
2) While still holding down the mouse button, drag the mouse around the fractal.
Notice that the white line (representing the path taken by the point being calculated) seems to come back very close to its starting point. It gets into a cycle, continually looping around the same path.
If the status bar is visible, Fractal eXtreme calculates the length of the cycle (that is, how many iterations it takes before the calculations end up at the same point twice. You should notice that the calculation path does a cycle of length three! Gosh, what a surprise? I wonder if this pattern holds? Of course it does!
3) It's interesting to note that if you go to the smaller bulb between the three bulb and the four bulb, the cycle is (of course) seven lines long, but (if you zoom out enough to see the entire cycle) you will see that it goes around twice, instead of just once, like all of the bulbs in the main sequence.
4) If you drop down to the next level of bulbs, the calc path goes around three times.
So, it appears that you can tell how many cycle lengths are being added up, by viewing a calc path's number of orbits.
To continue with Part 3 of this exercise, click here.