Ordered and chaotic superlattices have been identified in Nature that give rise to a variety of colours reflected by the skin of various organisms. In particular, organisms such as silvery fish possess superlattices that reflect a broad range of light from the visible to the UV. Such superlattices have previously been identified as 'chaotic', but we propose that apparent 'chaotic' natural struc...

The traveling salesman problem is a problem of finding the shortest tour through given points. In 1959, Beardwood, Halton, and Hammersley studied asymptotic length of the shortest tour through points on Euclidean space. In particular they described the optimal tour length with Euclidean dimension for the case that points are distributed with respect to Lebesgue absolutely continuous measure. In...

Visual forms come in countless varieties, from the simplicity of a sphere, to the geometric complexity of a face, to the fractal complexity of a rugged coast. These varieties have been studied with mathematical tools such as topology, differential geometry and fractal geometry. They have also been examined, largely in the last three decades, in terms of mereology, the study of part-whole relati...

Over the years engineers have often looked to nature for inspiration when seeking new and innovative ways to solve complex design problems. For instance, the development of fractal geometry was originally inspired by studying the shapes of natural objects such as trees, leaves, ferns, terrain, coastlines, snowflakes, and cloud boundaries. Neural Networks (NN) have been developed to mimic the hu...

A novel fractal design scheme has been introduced in this paper to generate microstrip bandpass filter designs with miniaturized sizes for wireless applications. The presented fractal scheme is based on Minkowski-like prefractal geometry. The space-filling property and self-similarity of this fractal geometry has found to produce reduced size symmetrical structures corresponding to the successi...

Fractal antenna, as name concerns, uses fractal i.e. structure does not change and repeat it when large focus has created upon it. This repetition feature of this antenna provides a great flexibility that it can be designed and can used in different frequencies. These antennas gives a finite area of coverage but the diameter of perimeter becomes infinite. Fractal antenna is used in most of the ...

A innovative geometry of fractal microstrip antenna has proposed which can be used for various multiband applications. This hexagonal fractal antenna structure has designed to produce multiband characteristics or to achieve miniaturizations. Multiple hexagons of the proposed geometry of an antenna are interconnected to maintain conductivity and to preserve electrical self-similarity. The hexago...

Trying to combine fractal geometry and solid modeling seems to be a contradiction in itself, In this paper a new type of 3D objects is presented that accomplishes this combination in a specific way. Objects with a fractal macro structure and a 3D solid micro structure can be specified and rendered efficiently by using context free, attribute, geometric grammars. This new object type can be inco...