What I'm going to talk about today:

1. Moving from one dimension to two.
2. x,y co-ordinates, area, Pythagoras' theorem.
3. Circles, Sine, Cosine and Pi.
4. Two dimensional lists (or arrays) for remembering pixels.
5. Delaunay triangulation / Voronoi diagram.
6. Bonus: Art from Rules.

1. Moving from one dimension to two.

• Going from a line to a square.
• Artwork: Flatland by Edwin Abbott Abbott.

2. x,y co-ordinates, area, Pythagoras' theorem.

• (x,y) pairs are Cartesian co-ordinates in Euclidean space.
• Y on computers is the opposite way to the way you learnt in school - because old computers scanned from the top down using Cathode Ray Tubes.
• Area - if you double the width and the height, area scales x4 NOT x2.
• Pythagoras' theorem - see proofs on Wikipedia page and Better Explained. P.S. Better Explained is AWESOME!

3. Circles, Sine, Cosine and Pi

• What is a circle? "It is the set of all points in a plane that are at a given distance from a given point".
• A Gentle Introduction To Learning Calculus from Better Explained.
• Intuitive Understanding of Sine Waves.
• Sine and cosine and tan aka Trigonometry again, from Better Explained.
• Bonus! Online version of the fantastic book, Calculus Made Easy - sample quote - "Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can".

4. Two dimensional lists (or arrays) for remembering pixels.

• 2D arrays, or arrays of arrays.
• Artwork: Every Icon (1997) John F. Simon, Jr. New York Times article about the artwork.
• Question, how might you store a two dimensional array within a one dimensional one?

5. Delaunay triangulation / Voronoi diagram.

• The Voronoi diagram is the diagram of boundaries between a set of points such that within the boundaries, one is closer to that point than any other.
• The Delaunay triangulation is the diagram of triangles of the Voronoi diagram such that no triangle is within another.
• The Voronoi diagram interactively.
• Artwork: Boundary Functions by Scott Snibbe.

6. Bonus: Art from Rules.

• My favourite is Agnes Martin. The Tate Modern on Agnes Martin (great quote!) .
• Sol LeWitt was a pioneer in minimalist and conceptual art, drawing up rules or algorithms that then could be carried out by anyone - "The system is the work of art; the visual work of art is the proof of the system"
• History of Design Systems by Rune Madsen has a series of references on Sol LeWitt and others.
• Great recent article on Generative Art by Jason Bailey.
• Solving Sol, Javascript implementations of his works.
• Generative Machines with Matt DesLauriers - great talk by a contemporary practitioner on their practice and inspirations.

Thanks!

• Follow me on Insta! I follow back: @jgl
• Get in contact via: www.joelgethinlewis.com
• Website:
  https://jgl.github.io/ComputationalThinking2021
• Today's slides:
  https://jgl.github.io/ComputationalThinking2021/lecture2.html