Fractal

Sciences exist to demonstrate the fundamental order underlying nature. Chaos/complexity theory is a novel and amazing field of scientific inquiry. Notions of our everyday experiences are somehow in connection to the laws of nature through chaos/complexity theory’s concerns with the relationships between simplicity and complexity, between orderliness and randomness (Retrieved from http://www.inclusional-research.org/comparisons4.php). It is interested in how disorder leads to order, of how complexity emerges in nature. There appears to be many striking and eye-catching similarities between the new science of chaos/complexity and education. An understanding of chaos/complexity theory seems almost crucial to our general understanding of education and teachers’ and students’ needs within educational systems. Chaos/complexity theory raises some very significant issues in an educational context, including responsibility, morality and planning; the significance of non-linear learning organizations; setting conditions for change by emergence and self-organization; the role of feedback in learning; changing external and internal environments(Morrison, 2006); it emphasizes on the fact that schools and learners as open, complex adaptive systems; cooperation and competition; pedagogy; and the significance of context (Larsen Freeman, 1997).This paper tries to provide an overview of this science and how it can inform education

The Sierpinski triangle is a fractal that is commonly used due to some of its characteristics and features. The Forex financial market is among the places wherein this triangle's characteristics are effective in forecasting the prices and their direction changes for the selection of the proper trading strategy and risk reduction. This study presents a novel approach to the Sierpinski triangle and introduces an innovative model based on it to forecast the direction changes in currency pairs, particularly EUR/USD. The model proposed in this study is dependent on the number of data selected for forecasting. The number of data is, in fact, the area of the initial triangle and the forecasted value of the self-similar triangles formed in each stage. For the performance assessment of the proposed method within one year (03/01/2019 to 28/02/2020), daily EUR/USD closed price data was classified into three categories, namely the training (70%), testing (20%), and validation (10%). Three approaches were proposed that led to forecasting the mean direction accuracy and the best result of over 60 percent in the third approach and over 50 percent in the first and second approaches. Results reflect the satisfactory improvements in the third approach compared to the econometrics, time-series, and machine learning methods. Moreover, the optimal number of data for the model is selected such that the difference between the accuracy of the direction forecasting in the training category and testing category is above 0.6 and below 0.05.

The Islamic era is the period of new s tyles and beyond its own time. Shamsa, Muqarnas, S tar, geometric motifs, and decorative elements have fractal nature, which was used as a tool to express the architect’s idea by repeating the same components in a spatial dimension. We will reach the effect of Islamic impacts on fractal architecture and semantic cognition, and by finding the roots of theories about fractal with an analytical-descriptive approach, we will unders tand the relationship between fractals and how they are used by architects. Our focus is on comprehensive s tudy and calculation, not only in ornaments but also in s tructure, to find patterns of fractal form, to represent coordination between components. Firs t, we proved and extracted the fractal properties and patterns between the cons tituent elements, including self-similarity, repeatability, small-scale, and non-integer dimension, using visual analysis, and then we set up the Box-counting analysis technique with two purposes of calculating fractal dimension and finding their relationship. Aware of the mathematical proportions and relationships between the components of nature, the architect of the Sheikh Lotfollah Mosque has displayed the geometric sequence limit with an ascending equation in the interior ornaments of the dome. His goal is both to create the world of spirituality on a micro-scale and make it unders tandable for an observer. Thus, in this way, he has sometimes expressed his concept through mathematics, proportions, and sometimes by showing beliefs in concepts such as unity in diversity, all of which in their essence have concepts consis tent with fractal forms.