Fractals and Multifractals H1QZDSC70W
| URI | m2://res/H1QZDSC70W |
|---|---|
| Kind | course |
| Creators | M. Guru Prem Prasad Prof. A. Gowrisankar (instructor) |
| Date | 2026-07-10 |
| Scope | in |
| Ids | course 0022nd079:111103001 |
Expressions
e1: edition
| Language | en |
|---|---|
| Date | 2026-07-10 |
- m1: page, IIT Guwahati (record). nptel 111103001
- m2: page, 2026-07-10 (record). nptel 111103001
Contents
- part 1: Week 1: History of Fractals
- session 1: Lecture 1: Cantor set
- session 2: Lecture 2: Sierpinski Triangle, Von Koch Curve
- session 3: Lecture 3: Fractals and Examples
- part 2: Week 2: Compact and Complete Metric Space
- session 4: Lecture 4: Metric Space, Compact Metric Space
- session 5: Lecture 5: Sequence, Equivalent metrics
- session 6: Lecture 6: Continuous and Uniform Continuous Function, Homeomorphism
- session 7: Lecture 7: Cauchy Sequence, Complete Metric Space, Contraction Mapping
- part 3: Week 3: Fractal Space and Iterated Function System
- session 8: Lecture 8: Fixed Point, Banach Contraction Mapping Theorem
- session 9: Lecture 9: Hyperspace H(X), Hausdorff Metric
- session 10: Lecture 10: Hausdorff distance of two closed interval in R
- session 11: Lecture 11: Completeness of the Space of Fractals
- session 12: Lecture 12: Dilation of a Set and its Associated Properties
- session 13: Lecture 13: Iterated Function System (IFS), Contraction on H(X)
- part 4: Week 4: IFS Theory
- session 14: Lecture 14: Hutchinson-Barnsley Mapping and Its Properties
- session 15: Lecture 15: Deterministic Fractals and Examples
- session 16: Lecture 16: Condensation Set, Collage Theorem, Random Iteration Algorithm
- session 17: Lecture 17: Deterministic Algorithm
- part 5: Week 5: Fractal Interpolation
- session 18: Lecture 18: Classical Interpolation
- session 19: Lecture 19: IFS for Fractal Interpolation Function
- session 20: Lecture 20: Existence of Fractal Interpolation Function
- session 21: Lecture 21: Types of Fractal Interpolation Functions, Vertical Scaling Factor
- session 22: Lecture 22: Estimation of Fractal Interpolation Parameters
- part 6: Week 6: Fractal Interpolation
- session 23: Lecture 23: Variable Vertical Scaling Factors
- session 24: Lecture 24: Iteration in Fractal Interpolation
- session 25: Lecture 25: Integration in Fractal Interpolation
- session 26: Lecture 26: alpha Fractal Interpolation Function
- session 27: Lecture 27: Fractal Dimension
- part 7: Week 7: Fractal Dimension
- session 28: Lecture 28: Fractal Dimension
- session 29: Lecture 29: Estimation of Fractal Dimension
- session 30: Lecture 30: Box-counting Theorem
- session 31: Lecture 31: Box-counting dimension of Sierpinski Triangle, von Koch Curve and Cantor set
- part 8: Week 8: Fractal Dimension
- session 32: Lecture 32: Invariance of Fractal Dimension
- session 33: Lecture 33: Properties of Fractal Dimension
- session 34: Lecture 34: Fractal Dimension of an IFS Attractor
- session 35: Lecture 35: Fractal Dimension of a Fractal Interpolation Function
- part 9: Week 9: Topological Dimension and Hausdorff Dimension
- session 36: Lecture 36: Topological Dimension and Examples
- session 37: Lecture 37: Measuring Sets, Physical Interpretation of Hausdorff-Besicovitch Dimension, Hausdorff Dimension of von Koch curve
- session 38: Lecture 38: Diameter of a Set, δ-cover of a Set, s-dimensional Hausdorff measure
- part 10: Week 10: Hausdorff Measure and Hausdorff Dimension
- session 39: Lecture 39: Scaling property, Holder condition, Hausdorff Dimension, Properties of Hausdorff dimension
- session 40: Lecture 40: Calculation of Hausdorff dimension, Equivalent definition of Hausdorff dimension
- session 41: Lecture 41: Estimation of Hausdorff measure, Hausdorff Dimension and Examples
- session 42: Lecture 42: Dimensions of Self-Similar Sets
- part 11: Week 11: Multifractal Measure
- session 43: Lecture 43: Conserved Quantity in the Triadic Cantor Set
- session 44: Lecture 44: Legendre transformation, Theory of multifractality
- session 45: Lecture 45: Dyadic Cantor set, Deterministic Multifractal
- session 46: Lecture 46: Cut and Paste model on Dyadic Cantor Set
- part 12: Week 12: Random Fractals
- session 47: Lecture 47: Dyadic Sierpinski Triangle, Cut and paste model on Sierpinski carpet
- session 48: Lecture 48: Multifractal Measure on the Koch Curve, Multifractal Measure on the Sierpinski Carpet
- session 49: Lecture 49: Curdling and the Devil’s Staircase, Curdling with Several Length Scales, Generalized Fractal Dimensions
Catalogue records
- nptel: 111103001 (manifestation)
- nptel_video: 111103001 (manifestation)