# The Fractal Logic of ARTriangles

ARTriangles products are probably the most sophisticated mosaic tiling systems ever offered. In order to become familiar with the fractal symmetry embodied in these shapes, it is useful to perform a few basic manipulations.

Based on the Golden or Divine Proportion, the acute triangle consists of two long sides and one short. The obtuse triangle has two short sides and one long.

For the first exercise, arrange ten acute triangles into a circle.

Next arrange ten obtuse triangles into a star made of five mirrored tiles.

An infinite number of mosaic designs can be created with various pieces of these stars and circles. Start simple and see what each of these triangles can do.

You can make stars with five acute triangles that spin two ways.

You can also make a circle or ring with ten obtuse triangles.

These examples illustrate the property of radial symmetry, an important aspect of these triangles. It contributes to fractal logic that becomes increasingly apparent when shapes are used together.

Once they’re assembled, you can see why the triangles work so nicely together. The fractal quality becomes evident when we see the way they combine.

Now that we have put some of the fractal logic basics into practice, we can expand some possible combinations. You should be able to see how Fractal Logic resides in the proportions of these star and circle symmetries, and can further explore how they logically self-arrange into infinite varieties that always fit together.

To fully utilize their fractal nature we have provided triangles in several scales. Fractals are always scalable so the larger matches the smaller. The purpose of this medium is to inspire creativity through intuitive placing of the triangles.

We supply many examples but our goal is to have you experience the delight of originality. Exercise that part of your brain that uses intuition to find out where these fascinating shapes can lead.

You will benefit from the hand-to-eye coordination involved while enjoying the fun of discovering infinite possibilities.