Metamaterial model of fractal time

Terahertz electric response of fractal metamaterial structures

The electromagnetic response of H-fractal structures, consisting of self-similar metallic lines or slits in metallic films deposited on silicon substrate, has been investigated in the terahertz region. The subwavelength fractal structure was observed to display electric resonances, with redshift in the resonant frequencies accompanying an increase in either the fractal level or the sample size....

A Fractal Forecasting Model for Financial Time Series

Financial market time series exhibit high degrees of non-linear variability, and frequently have fractal properties. When the fractal dimension of a time series is non-integer, this is associated with two features: (1) inhomogeneity— extreme fluctuations at irregular intervals, and (2) scaling symmetries— proportionality relationships between fluctuations over different separation distances. In...

Fractal Quantum Space -Time

In this paper we calculated the spectral dimension of loop quantum gravity (LQG) using the scaling property of the area operator spectrum on spin-network states and using the scaling property of the volume and length operators on Gaussian states. We obtained that the spectral dimension of the spatial section runs from 1.5 to 3, and under particular assumptions from 2 to 3 across a 1.5 phase whe...

Real Time Fractal Landscape Flyover

Fractal and Multifractal Time Series

5 Methods for Non-Stationary Fractal Time-Series Analysis 15 5.1 Wavelet Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 15 5.2 Discrete Wavelet Transform (WT) Approach . . . . . . . . . . 16 5.3 Detrended Fluctuation Analysis (DFA) . . . . . . . . . . . . . 16 5.4 Detection of Trends and Crossovers with DFA . . . . . . . . . 19 5.5 Sign and Magnitude (Volatility) DFA . . . . . . . ....