A Dendrite Example

This fractal is a dendrite because it is connected, contains no loops (removing any point except a branch tip disconnects it), and has infinitely many branch points.

As an example of a branch point, take the fractal to be in the unit square. Then the point (1/2, 1/2), where the green and red regions meet, is a branch point.

The line from (0,1) to (1/2, 1/2) splits into two branches, one from (1/2, 1/2) to (1, 0), the other from (1/2, 1/2) to (1, 1/2).

As suggested by the colors on the right, the dendrite is made of three copies of itself, each a copy of the original, scaled by a factor of 1/2 in the x- and y-directions, and in different orientations and positions.

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