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ETC is the Encyclopedia of Triangle Centers, where a large collection of well defined triangle points are defined. As of this time (Apr 2026) there are well over 70,000 triangle centers. Clearly, we will deal with just a handfull.

Step 1: We begin with a Hexagon containing a random point. It is the only time we will pick a random point. Next, we select a random side of the hexagon. Then we connect our point to the two ends of the selected side, forming a triangle. Nothing is sketched or graphed to now.

Step 2: Next we find the center of that triangle and finally, that point is graphed. Sometimes the selected point is inside the hexagon, but not always.

Step 3: Now select again a random side of the hexagon. Create a triangle from the previosuly graphed point and the two ends of the randomly selected side.

Step 4: Go back to Step 2

Do the above steps 2 to 4 thousands of times.

How to Use the Interface

The upper left Clear Button clears all points from the graph, leaving the hexagon and its center shown. The Clear Text button clears text that might be made with the "check" button, to be explained in a bit.

The Number of Points is an input box that defaults to 40000. You can change it to nearly any number.

Number of Points on the Canvas is just a count of how many points are displayed.

Color Use any valid color name, or hex value preceded with #, such as #FF0000

In the dropdown box, select a triangle center type. The X(#) refer to ETC numbering. After selecting a triangle center, press Make Fractal

If you have a fast enough computer (the calculations are done in your browser!!), After a few seconds you will see the fractal.

Important: Each time you press the Make Fractal button, a new block of points is added to the existing block. For a bit, that will make the points darker, since they won't likely get added in exactly the same place. Interestingly you can select a triangle center such as "Nagel Point" and click Make Fractal a few times, then without using Clear, select a different triangle center, such as Feuerbach Point, and click Make Fractal again, resulting in the two Fractals graphing over the top of one another.

Check Button This button will print some triangle coordinates and the centerpoint coordinates for the chosen triangle type. You clear this text with the clear text button. You an use these data points to try and solve for a center point yourself.

Orthocenter : Works fine! Just doesn't happen to make a fractal by this method.

Credit to John D. Cook for this idea.