Fractal Geometry – Spidron

A spidron is a plane figure consisting of an alternating sequence of equilateral and isosceles (30°, 30°, 120°) triangles. Within the figure, one side of a regular triangle coincides with one of the sides of an isosceles triangle, while another side coincides with the hypotenuse of another, smaller isosceles triangle. The sequence can be repeated any number of times in the direction of the smaller and smaller triangles, and the entire figure is centrally projected through the mid-point of the base of the largest isosceles triangle.

The semi-spidron is half of the spidron, consisting of increasingly densely packed and smaller regular and isosceles triangles. The sequence can also be continued in the opposite direction, with ever larger triangles, ad infinitum. It seems to me that this composition, or to use the term that is more customary in mathematics, this “triangle complex”, or the half of it I call a semi-spidron is the foundation for all the other shapes with their interesting spatial and almost “spatially flexing” properties which – according to the comments and the feedback I get – promise novel developments in the fields of geometry, physics and other branches of science.
Source: http://edan.szinhaz.org//SpidroNew/general_concept.htm