CSC4700-Fractals

This lecture introduces fractals, focusing on their mathematical basis, visual representation, and implementation in C++. Mandelbrot set is used as a prime example, demonstrating how to generate fractal images using C++ code and exploring parallel computing techniques for optimization. The lecture also touches upon complex numbers and different parallel computing paradigms.

[00:00:00] - Intro
[00:00:26] - Introduction to Parallel Computing
[00:01:28] - Lecture Overview: Math and Fractals
[00:02:02] - Fractals: Definition and Nature
[00:08:10] - Psychedelic Fractals and Mandelbrot Set
[00:11:15] - Complex Numbers Refresher
[00:16:02] - C++ Support for Complex Numbers
[00:20:48] - Mandelbrot Set: Theory and C++ Implementation
[00:25:00] - Visualizing Mandelbrot Set Computationally
[00:33:35] - Parallelization and Fork-Join Parallelism
[00:40:12] - Parallelization in C++: Execution Policies
[00:42:39] - Applying Parallel Algorithms to Mandelbrot
[00:45:28] - Julia Set: Related Fractal
[00:47:09] - Flynn's Taxonomy and Parallel Architectures
[00:53:14] - SIMD and Vectorization Fundamentals
[00:56:07] - SIMD in C++: std::experimental::simd
[01:00:46] - Conditional Operations and SIMD Masks
[01:04:02] - Applying SIMD and Vectorization to Mandelbrot
[01:09:35] - C++ SIMD Execution Policies and HPX
[01:11:32] - Vectorized Mandelbrot Implementation
[01:15:06] - Final Vectorized and Parallel Implementation
[01:16:17] - Monte Carlo Estimation of Mandelbrot Area
[01:17:14] - Conclusion and Final Remarks