A hybrid Example

This fractal is not connected because the green part is separated from the red and blue parts.

On the other hand, the red and blue parts have a point in common.

That point belongs to the line from (0, 1/3) to (1, 1/3), part of the fractal.

Self-similarity and the disconnect between the green part and the red and blue parts guarantees the fractal has infinitely many components: it is far from connected.

Yet this is not a Cantor set, because it contains infinitely many line segments.

Hence the name hybrid. Suggestions of alternative terminology are welcome.

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