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In this compilation, the authors begin with a description of fractal geometry, its property of self-similarity, and how its processes of bifurcation can appear in the arts and architecture. These fractal features are common in different cultures and in different architectural styles. Next, the role of algebraic curves in painting, sculpture, and architecture is discussed. They discuss an art world devoted to the entanglement phenomenon through modifying the perception of space, approaching new horizons educational fields. An investigation of the function and characteristics of fog in various paintings by famous artists of different art movements (in which the presence of fog significantly affects the visual experience) is provided. Following this, the authors describe where fractality appears in architecture and in urban organization, opening new opportunities in virtual architecture and hyperarchitecture. An additional paper presents a study on complexity in architecture. Afterwards, this book aims to show how and where the concept of time can be applied in architecture, maintaining that time is a parameter which architects seldom consider in their projects. The authors go on to illustrate some properties using Markov matrices, open symbolic dynamic nets, and fields on Julia sets, finding find both symmetrical and spiral patterns on local regions of Julia sets, and discontinuous series in the dynamics of some region that are recordable in the neurophysiology of intermittent consciousness. The book goes on to cover, new Koch curves, new Sierpinski curve, Julia sets ,new Hilbert curves , Mandelbrot and Julia sets , Gingko leaf and techniques to generate Sierpinski Gasket and Sierpinski Carpet as 3- variable and as 4-variable fractals respectively using superior iterates for contractive operators are described.

Geometry in art. --- Fractals in art. --- Geometry in architecture.

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This book focuses on the control of fractal behaviors in nonlinear dynamics systems, addressing both the principles and purposes of control. For fractals in different systems, it presents revealing studies on the theory and applications of control, reflecting a spectrum of different control methods used with engineering technology. As such, it will benefit researchers, engineers, and graduate students in fields of fractals, chaos, engineering, etc.

Julia sets. --- Nonlinear control theory. --- Fractional differential equations. --- Engineering. --- Complexity, Computational. --- Control engineering. --- Complexity. --- Control. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Extraordinary differential equations --- Differential equations --- Fractional calculus --- Control theory --- Nonlinear theories --- Sets, Julia --- Fractals --- Control and Systems Theory. --- Construction --- Industrial arts --- Technology --- Computational complexity. --- Statistical physics. --- Physics --- Mathematical statistics --- Control engineering --- Control equipment --- Engineering instruments --- Automation --- Programmable controllers --- Complexity, Computational --- Electronic data processing --- Machine theory --- Statistical methods