A pentagram has the proportions of the golden ratio integrated in its geometry. Each line segment forms this ratio with the adjacent line segment, making the pentagram self-similar and thus fractal.
In this design you see a number of different ways in which the fractal nature of a pentagram can be depicted. Small pentagrams with the ratio 1: φ (1,618 …) can be seen in the points of the large pentagram. This can be repeated indefinitely, because the last pentagram can never reach the absolute point of the pentagram.
An inverted pentagram fits in the middle of the large pentagram. This can be repeated indefinitely, with the result that the golden ratio proportion can be indefinitely reduced in scale.
This five-fold symmetry of a pentagram can be found in the five-fold seed pattern of an apple. The size of this seed pattern compared to the size of the apple is like the small, inverted pentagram to the large pentagram.
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