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.

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

• 2D arrays, or arrays of arrays.
• Artwork: Every Icon (1997) John F. Simon, Jr.
• 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, who now works for Facebook.

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.

Thanks!

• More about me: @joelgethinlewis
• Get in contact via: www.joelgethinlewis.com
• Website:
  https://jgl.github.io/ComputationalThinking2019
• Today's slides:
  https://jgl.github.io/ComputationalThinking2019/lecture2.html