| Outlines may be captured as rectangular coordinates or Fourier coefficients and, even when non-fractal, analysed in terms of fractal dimensions. |
|
| The result is a division of the initial planar shape into several pieces with ragged fractal edges. |
|
| The Von Koch snowflake is a fractal which is constructed from an equilateral triangle as follows. |
|
| You see infinitely detailed multicoloured fractal alphabets, they see growing paisley patterns. |
|
| This is an example of what is known as a fractal set since its dimension is not a whole number. |
|
| Data from a field study were re-examined to test the utility of fractal analysis. |
|
| A number of fractal dimension algorithms were developed and evaluated using a field data set of 100 incidents. |
|
| Then we study the technique formally, and then apply it to images of fractal art. |
|
| To explain the concept of fractal dimension, it is necessary to understand what we mean by dimension in the first place. |
|
| It should be remembered that in his era there was little thought or knowledge of fractal geometry, curved space or different degrees of infinity. |
|
| The fractal shape and rounding of DPTAP domains indicate that domain growth occurred relatively isotropically. |
|
| More precisely, the recursive nature, which is essential for fractal models, is lacking in the procedural approach. |
|
| This result also solved a long-standing open problem concerning the existence of certain fractal sets in the plane. |
|
| Furthermore, could we explore the idea of the body as a dynamic nonlinear hologram existing within a fractal space? |
|
| While classical geometry assumes that objects exist in integer dimensions, fractal geometry deals with objects that have non-integer dimensions. |
|
| When the game starts, your selected object is presented in the center of a spherical space bounded by fractal walls. |
|
| A structure may be called fractal if it presents the same irregularity at all scales. |
|
| His research focuses on the interplay between fractal geometry and stochastic processes. |
|
| A fractal is a mathematical object that is self-similar irrespective of scale. |
|
| It would appear that the duration of microstates plays a predominant role in this fractal organisation of thought. |
|
|
|
| His unique knowledge of subjects such as fractal dynamics, subspace theory, a tri-vector system and others, has made this energetic feedback system possible. |
|
| The first condition that must be fulfilled to apply scaling analysis techniques is that the growth behavior of a process lie in the fractal nature of the interface. |
|
| To sculpt is for me like entering a fractal world, a kind of black hole where my obsession for the details knows no bound. |
|
| The spectrum yields a classic fractal object called a Julia set. |
|
| If all these were not just a series of fortuity, the universe could be said to be consecutive vertically in a fractal structure. |
|
| This allows the decoding process to be started with an arbitrary image which converges to a fractal approximation of the original picture. |
|
| If I buy my computer to send email with, and I want to make fractals, I don't have to buy a new fractal machine. |
|
| The use of chaos theory and fractal dimension analysis is widespread. |
|
| This animation is a fractal world in which we can zoom in or away with a slider in the top left of the page. |
|
| The mathematical object known as a fractal is made up of parts that have exactly the same structure as it itself, and so on ad infinitum. |
|
| This connection to nature has no doubt also contributed to the popularity of fractal geometry. |
|
| In cosmopolis, Packer Capital uses complex fractal modeling, based on patterns in nature, to map data in the markets. |
|
| With these branching patterns, roots can be characterized by fractal analysis over a range of scales from about a quarter of a millimetre to several centimetres. |
|
| That, at bottom, is what describes a fractal. |
|
| There are also fractal motifs in some Celtic jewellery. |
|
| With its many unpredictable twists and turns, but governed by an unseen logic, it is tempting not to mention fitting to liken the course of his life to a fractal. |
|
| Steeped in the intricacies of catalytic crackers and fractal geometry, Dr. Siauw Ng is a world-travelling scientist who has left an indelible Canadian mark on the global oil and gas industry. |
|
| The geometry of external material of the wall, DektonA, forms a contemporary fractal pattern related to the Golden Section. |
|
| With its fizzing fringe of crystal-like microforms blossoming out of a conjunction of black circles, this fractal pattern looks crazy but is the outcome of geometrical calculations. |
|
| According to chaology, fractal forms of management and control are essential. |
|
|
|
| In our June 11th comparison of IBM and the Carnegie Corporation we wrongly awarded a Nobel prize to Benoît Mandelbrot, the pioneer of fractal geometry. |
|
| In 1975 he invented the word fractal to describe his discoveries. |
|
| If we compare the authentication process using hash function and fractal geometry, we find that in many ways are similar. |
|
| As this organism grew, the number of compartments remained constant, but each expanded and folded in a fractal pattern according to the terminology of the mathematician Benoit Mandelbrot. |
|
| The method has successfully been applied to accurately determine morphology and fractal structure of large aggregates of soot particles based on TEM images. |
|
| The results showed that maize roots indeed have fractal properties, such as self-similarity across various scales. |
|
| Random polarization returns usually indicate a fractal surface, such as rocks or soil, and are used by navigation radars. |
|
| In this study, the species pool size and the fractal nature of ecosystems were combined to clarify some general patterns of this gradient. |
|
| In this way, it is possible to build fractal hypervolumes, whose fractal dimension rises up to three moving towards the equator. |
|
| In this respect, fractal geometry has been a key utility, especially for mosques and palaces. |
|
| It also replaces the rather 1960s-ish gestalt cubes cover art of the first two editions with a fractal representation of swirly Mandelbrot sets. |
|
| Changes in electroencephalograph fractal dimension over time were studied by measuring the correlation dimension. |
|
| Future research will become increasingly important for multi-dimensional fractal structures, in particular, variations and Julio Mandelbrot sets. |
|
| Effect of tillage on fractal indices describing soil surface microrelief of a Brazilian Alfisol. |
|
| It can be expressed by other derived parameters such as sinuosity, curvature, tortuosity, curviness, or fractal dimension. |
|
| At the glass transition point, roughly half of the molecules are in the solid state, and crystalline clusters make a fractal pattern. |
|
| The system is based on polynomial fractal sets, specifically on the Mandelbrot set. |
|
| Ashton Raggatt McDougall began to muck about with fractal geometries in architecture a decade ago. |
|
| Aside the fact that the object looks fractioned, the term fractal was given due to the strange fact that these objects have a dimension which is not a whole number but a fraction. |
|
| Finally, the observed fractal shape of sutured quartz grain boundary has its implications for geothermometry. |
|
|
|
| Having defined the necessary tools for studying fractal structures, it is now time to get to the heart of the matter by giving the first concrete examples of fractals. |
|
| Down in the galleries, giant jumbo screens offer a fractal imagery of a chase scene involving herds of pachyrhinosaurus, hadrosaurs and the carnivorous gorgosaur. |
|
| Design and realizations of miniaturized fractal RF and microwave filters. |
|
| Therefore, a fractal description has the potential to considerably simplify the statistical approach, and be a valuable addition to methods based on Euclidian geometry. |
|
| The design, by Lab Architecture Studio and Bates Smart, has shardlike clusters of buildings with fractal triangular designs on the facade in glass, zinc and sandstone. |
|
| Bedrock rivers typically flow in either a fractal pattern, or a pattern that is determined by weaknesses in the bedrock, such as faults, fractures, or more erodible layers. |
|
