Search results for "fractal curve"
showing 3 items of 3 documents
Espaces tangents pour les formes auto-similaires
2013
The fractal geometry is a relatively new branch of mathematics that studies complex objects of non-integer dimensions. It finds applications in many branches of science as objects of such complex structure often poses interesting properties. In 1988 Barnsley presented the Iterative Func-tion System (IFS) model that allows modelling complex fractal shapes with only a limited set of contractive transformations. Later many other models were based on the IFS model such as Language-Restricted IFS,Projective IFS, Controlled IFS and Boundary Controlled IFS. The lastto allow modelling complex shapes with control points and specific topol-ogy. These models cover classical geometric models such as B-…
Optical-Microwave Sensor for Real-Time Measurement of Water Contamination in Oil Derivatives
2023
This paper presents a novel microwave sensor using optical activation for measuring in real-time the water contamination in crude oil or its derivatives. The sensor is constructed from an end-coupled microstrip resonator that is interconnected to two pairs of identical fractal structures based on Moore curves. Electromagnetic (EM) interaction between the fractal curves is mitigated using a T-shaped microstrip-stub to enhance the performance of the sensor. The gap in one pair of fractal curves is loaded with light dependent resistors (LDR) and the other pair with microwave chip capacitors. The chip capacitors were used to increase the EM coupling between the fractal gaps to realize a high Q-…
Tangents to fractal curves and surfaces
2010
International audience; The aim of our work is to specify and develop a geometric modeler, based on the formalism of iterated function systems with the following objectives: access to a new universe of original, various, aesthetic shapes, modeling of conventional shapes (smooth surfaces, solids) and unconventional shapes (rough surfaces, porous solids) by defining and controlling the relief (surface state) and lacunarity (size and distribution of holes). In this context we intend to develop differential calculus tools for fractal curves and surfaces defined by IFS. Using local fractional derivatives, we show that, even if most fractal curves are nowhere differentiable, they admit a left and…