Background
Brocade is a multidisciplinary consultancy that collaborates with purpose-driven organizations to tackle intractable issues through strategic facilitation, data science, interpretive planning, and deep engagement.
Just as the "unknot" in knot theory represents the simplest, most fundamental form of a knot, Brocade helps organizations untangle complex issues to reveal clear, actionable paths forward.
Understanding the Unknot
In knot theory, an unknot is the simplest type of knot: a loop that can be smoothly transformed into a standard circle without any crossings or tangles. It serves as a fundamental concept in mathematical topology, representing a knot that is equivalent to a simple, untwisted loop.
As part of the process, Cotton examined the academic research and formulae behind the unknot to crack the code on replicating an unknot using Javascript alone.
Knot theory distinguishes between two types of knots. Unlike a knot, an 'unknot' can be simplified into a simple circle using simple moves like twisting, looping, and bending.
The Two Types of Unknots
In knot theory, there are two kinds of unknots: easy unknots, which can be identified and untangled with simple "Reidemeister" moves, such as loops and crossovers, and hard unknots, which require increasing their complexity before they can be simplified into a simple loop. Cotton created a solution for both types of unknots using two different Javascript algorithms.
Type 1: The Easy Unknot
The "Easy" unknot can be identified and untangled with simple Reidemeister moves, such as loops and crossovers. With these moves alone, the outputs are already quite varied.
Type 2: the "Hard" Unknot
The "Hard" unknot is so complex that it often times gets mistaken for an unsolvable knot. In knot theory, an unknot must be made more complex before it will simplify.
Coding Process
Web graphics are typically dominated by rectangular and blocky shapes, rendering the creation of organic, curved forms both uncommon and challenging. Cotton translated the complexities behind unknotting theory into a smooth generative drawing of an unknot. Different every time, and infinitely generative, the unknot is still rendered as elegant, curved, and most importantly—unexpected for the web.
Outputs & Applications
Cotton implemented the generative graphic as a storytelling mechanism and an ownable brand motif throughout Brocade's touchpoints.
Custom Generator
A custom client-facing unknot generator tool was also developed for the Brocade team to create various unknots for different applications.
Creative Director
Talia Cotton
Designer & Coder
Noah Schwadron