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Lecture 13 of 49Week 3: Fractal Space and Iterated Function System
Lecture 13: Iterated Function System (IFS), Contraction on H(X)
Prof. M. Guru Prem Prasad Prof. A. Gowrisankar · IIT Guwahati
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All the lectures
- Lecture 1: Cantor set
- Lecture 2: Sierpinski Triangle, Von Koch Curve
- Lecture 3: Fractals and Examples
- Lecture 4: Metric Space, Compact Metric Space
- Lecture 5: Sequence, Equivalent metrics
- Lecture 6: Continuous and Uniform Continuous Function, Homeomorphism
- Lecture 7: Cauchy Sequence, Complete Metric Space, Contraction Mapping
- Lecture 8: Fixed Point, Banach Contraction Mapping Theorem
- Lecture 9: Hyperspace H(X), Hausdorff Metric
- Lecture 10: Hausdorff distance of two closed interval in R
- Lecture 11: Completeness of the Space of Fractals
- Lecture 12: Dilation of a Set and its Associated Properties
- Lecture 13: Iterated Function System (IFS), Contraction on H(X)
- Lecture 14: Hutchinson-Barnsley Mapping and Its Properties
- Lecture 15: Deterministic Fractals and Examples
- Lecture 16: Condensation Set, Collage Theorem, Random Iteration Algorithm
- Lecture 17: Deterministic Algorithm
- Lecture 18: Classical Interpolation
- Lecture 19: IFS for Fractal Interpolation Function
- Lecture 20: Existence of Fractal Interpolation Function
- Lecture 21: Types of Fractal Interpolation Functions, Vertical Scaling Factor
- Lecture 22: Estimation of Fractal Interpolation Parameters
- Lecture 23: Variable Vertical Scaling Factors
- Lecture 24: Iteration in Fractal Interpolation
- Lecture 25: Integration in Fractal Interpolation
- Lecture 26: alpha Fractal Interpolation Function
- Lecture 27: Fractal Dimension
- Lecture 28: Fractal Dimension
- Lecture 29: Estimation of Fractal Dimension
- Lecture 30: Box-counting Theorem
- Lecture 31: Box-counting dimension of Sierpinski Triangle, von Koch Curve and Cantor set
- Lecture 32: Invariance of Fractal Dimension
- Lecture 33: Properties of Fractal Dimension
- Lecture 34: Fractal Dimension of an IFS Attractor
- Lecture 35: Fractal Dimension of a Fractal Interpolation Function
- Lecture 36: Topological Dimension and Examples
- Lecture 37: Measuring Sets, Physical Interpretation of Hausdorff-Besicovitch Dimension, Hausdorff Dimension of von Koch curve
- Lecture 38: Diameter of a Set, δ-cover of a Set, s-dimensional Hausdorff measure
- Lecture 39: Scaling property, Holder condition, Hausdorff Dimension, Properties of Hausdorff dimension
- Lecture 40: Calculation of Hausdorff dimension, Equivalent definition of Hausdorff dimension
- Lecture 41: Estimation of Hausdorff measure, Hausdorff Dimension and Examples
- Lecture 42: Dimensions of Self-Similar Sets
- Lecture 43: Conserved Quantity in the Triadic Cantor Set
- Lecture 44: Legendre transformation, Theory of multifractality
- Lecture 45: Dyadic Cantor set, Deterministic Multifractal
- Lecture 46: Cut and Paste model on Dyadic Cantor Set
- Lecture 47: Dyadic Sierpinski Triangle, Cut and paste model on Sierpinski carpet
- Lecture 48: Multifractal Measure on the Koch Curve, Multifractal Measure on the Sierpinski Carpet
- Lecture 49: Curdling and the Devil’s Staircase, Curdling with Several Length Scales, Generalized Fractal Dimensions