41.Sample answer: The leaves in the tree and thebranches of the trees are self-similar. These self-similar shapes are repeated throughout thepainting.42a.The flower and mountain are computer-generated; the feathers and moss are real.42b.The fractals exhibit self-similarity and iteration.43.See students’ work.44.In Stage 1, the shaded triangle has legs 3 and4 units. The hypotenuse has length c, where c23242, or c916 or 5. So, theperimeter of the triangle is 345 or 12 units.In Stage 2, there are three small shaded trianglesand the larger shaded triangle from Stage 1. Eachof the small shaded triangles has legs 2 and1.5 units. The hypotenuse has length d, where d2221.52, or d42.25 or 2.5. So, theperimeter of all shaded triangles in Stage 2 is 3(21.52.5)12 or 30 units.45.Sample answer: Fractal geometry can be found inthe repeating patterns of nature. Answers shouldinclude the following.• Broccoli is an example of fractal geometrybecause the shape of the florets is repeated
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