Sierpinski's forest: New technology of cool roof with fractal shapes

This paper presents a new technology for constructing cool roofs composed of fractal shapes. The roofs consist of many Sierpinski tetrahedron units and block 100% sunlight from a particular direction. The sunlight from other directions partly penetrates the roof, creating a leafy shaded area under the roof. Compared with ordinary flat roofs, these roofs greatly reduce surface temperature and consequently provide a cool environment without strong heat radiation. The fractal structure of the tetrahedron units is similar to that of natural trees. Three-dimensional measurements revealed that natural trees have a fractal dimension of approximately 2, which is similar to that of the Sierpinski tetrahedrons. In this study, fractal roofs made from different materials were tested at two sites. The results showed that they were very effective in reducing surface temperatures in sunlight.

► This paper presents a new technology of cool roof with fractal shapes.
► The roof consists of many Sirpinski tetrahedron units.
► This roof significantly reduces surface temperature compared with a flat roof.
► This structure is similar to natural trees.