slides.tex.md

% Rust Concurrency - Generating the Mandelbrot Set % Ian Channing https://github.com/ianchanning/mandelbrot % March 10, 2021

Taken from the Rust Book

Based on the Concurrency section of Chapter 2 (A Tour of Rust)

from the O'Reilly "Programming Rust" book.

Extra concurrency algorithms from https://github.com/ProgrammingRust/mandelbrot

Introduction

Rust.

Complex numbers and iterating complex numbers.

The Mandelbrot set.

Generating the Mandelbrot set with one processor.

The required changes to use multiple processors.

Fearless concurrency.

Rust

Fearless Concurrency

For experienced parallel programmers - faster development

For inexperienced - can gain the benefits without the danger

Borrow Checker

Immutable - no problem

Mutable within one function - no problem

Passing mutable values between functions - enforced rules

Iterating over the real numbers

A simpler, but very similar iteration

$$ \begin{aligned} z_{n+1} &= z_n^2 \\ \end{aligned} $$

We can do the same for complex numbers

Complex numbers and iterating complex numbers

Addition

$$ \begin{aligned} (a+bi)+(c+di)=(a+c)+(b+d)i \\ \end{aligned} $$

Multiplication

$$ \begin{aligned} (a+bi)\times(c+di) &= ac+(ad+bc)i+bdi^2 \\ & = (ac-bd)+(ad+bc)i \\ \end{aligned} $$

The Mandelbrot set

An easy way to generate fractals

Complex number $z$

$$ \begin{aligned} z &= a+bi \\ \end{aligned} $$

Iterate $z$ from 0, square it and add another complex number $c$

$$ \begin{aligned} z_0 &= 0 \\ z_{n+1} &= z_n^2+c \\ \end{aligned} $$

For some values of $c$, $z$ will stay within a distance of 2 from the origin

Those are 'in' the Mandelbrot Set

Mandelbrot set with one processor

Flatten out the 2D image into one very long array

Multiple processors

Parallel thinking

Fearless concurrency

Switch to parallel code with little changes

Mutexs - dangerous in other languages but safe in Rust

Specialised parallel constructs