Another approach that captures the complexity of the world around us is to use fractal tiles. For example, starting with a tessellation by hexagons, replace each line segment by three line …

Purpose To illustrate three simple methods for making fractals that tile the plane. Materials Drawing software with scale, rotate, and reflect options; IFS software. Conclusion The first …

The original shape tiles the plane, so also will each iterate, being made up of ever smaller copies of the original tile. To see the limiting tile has a fractal boundary, recall the area-perimeter …

The result is a fractal island, that we shall see is also a fractal tile. For familiar geometric shapes such as a square or circle, there is a simple relation between the area and the perimeter. If A 1 …

A tutorial on basic fractal geometry and a panorama of uses of fractals, with supporting software, laboratory exercises, and resources for teachers

A tiling is a collection of shapes (tiles) that fit together to cover the plane, without overlapping or leaving gaps. A fractal tiling or f-tiling is a tiling in which the arrangement of tiles is fractal. A …

In this paper, we demonstrate how our research findings regarding fractal tilings arose through the teaching of a geometry course, and describe the mathematical relationships between the …

The mathematician Niels Fabian Helge von Koch (1870-1924) invented a famous curve by iteratively breaking up a line segment into three line segments of equal length and by replacing …

What is a fractal? Fractals have self-similar properties. If a portion of a fractal object is enlarged, the magnified portion always resembles the original figure. E.g. coastal line of...

If all the tiles are regular and similar, only equilateral triangles, squares, and hexagons can be used, because each of their interior angles evenly divides 360. Any point in the plane can be …