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1, A fractal description originally developed by mathematician Michael Barnsley, has been adapted to digitally sampled audio.

2, Mackenzie went on to produce fractal sounds from sampled real world waveforms.

3, Keywords: fractal, nucleate boiling, floc, biological aggregates.

4, Benoit Mandelbrot pioneered fractal geometry.

5, Renormalization group method which calculates fractal dimension theoretically is the most useful tool when we study critical phenomena of phase transition.

6, Peano fractal display program, in the hope that everyone useful.

7, Fractal image coding is a very promising image compression technique.

8, The fractal dimension of the material fracture rises with the increase of whisker direction angle.

9, But the fractal video compression process exhibits a high natural parallelism as there exist data independence when computing the compression codes.

10, After the original image is maked to quadtree fractal coding, we embed watermarking into it by range blocks searching its most-matched domain blocks in different search regions.

11, Using calculation of fractal theory, the fractal dimensions of the core structure fracture in granite gneiss and lamprophyre in Chengbei 30 Archaean group buried hill reservoir are1.

12, MANDELBROT generate beautiful fractal graphics, one for each, can be magnified, each generated color images will change.

13, Fractal theory builds tight dialectic relations among nature, society and thought in higher level.

14, Drawing on chaos theory and fractal geometry, the author introduces the concept of fractal market analysis.

15, The way that the trunk of a tree divides into smaller and smaller branches and twigs is an approximate fractal pattern.

16, Mackenzie's technique uses a variant of Michael Barnsley's iterated function system, called a fractal interpolation function.

17, Figs. 2a,(http://sentencedict.com/fractal.html) b and c show successive waveform expansions of fractal processed wind noise.

18, There are movements of Rabari, swirls and swoops apparently random but fractal in nature.

19, In one of them, researcher Jonathan Mackenzie is using the ideas behind fractal geometry to synthesise sounds.

20, Ronell avoids the trap by proceeding in ever-decreasing circles - or fractal geometry, as it is now known.

21, And this paper offers a method of concrete beam cracks simulation based on L system of fractal theory, and provides us a new way to visualize and simulate concrete crack.

22, According to the fact that wavelet detail coefficients of random fractal signal are approximately uncorrelated, the method based on wavelet-based whitening filter .

23, The other methods include: The conventional method of spectrogram parameters, the zero-pole model and the fractal method, the latter two were proposed by the present authors before.

24, Further, through the phase space reconstruction of relating time series and fractal analysis, discussion to nonlinear evolution of the system with varying heating power is delivered.

25, This time consuming block matching procedure influences speed of fractal block coding.

26, From the value and control of structure to coastline , we can know that fractal shows not only the complicated of geological phenomena, but also the being of cause of geological formation in a sense.

27, In this paper, we study the hot issues of fractal image encoding.

28, The corresponding calculating program was written by MATLAB to calculate the fractal dimensions of box-counting in the morphology imagine of semi-solid primary phase in A356 alloy.

29, Graphic designers have lots of fun with the Mandelbrot set. There are several fractal geometry software programs available for download.

30, The multifractal growth process of the SEM images of catalyst surface is studied using fractal and multifractal theory.