Piet Mondrian and Image Representation

MyMondrian100dpi

Piet Mondrian was a pioneer of abstract art. He was a Dutch painter, famous for his minimalist abstract art. His series of grid-based paintings consisted of rectangles, some of solid primary colour, others white, separated by thick black lines. Experiment with Mondrian-inspired are like this one of mine, while also exploring different representations of images (as well as playing with maths).

We will use this image to give you the idea, but you could use your own images using different image representations, then get others to treat them as puzzles to recreate the originals.


Vector Images

One way to represent an image in a computer is as a vector image. One way to think of what a vector representation is, is that the image is represented as a series of mathematically precise shapes. Another way to think of it is that the image is represented by a program that if followed recreates it. We will use a simple (invented) language for humans to follow to give the idea. In this language a program is a sequence of instructions to be followed in the order given. Each instruction gives a shape to draw. For example,

Rectangle(Red, 3, 6, 2, 4)

means draw a red rectangle position 3 along and 6 down of size 2 by 4 cm.

ExplainingInstructionsRectangle is the particular instruction giving the shape. The values in the brackets (Black, 3, 6, 2, 4) are arguments. They tell you the colour to fill the shape in, its position as two numbers and its size (two further numbers). The numbers refer to what is called a bounding box – an invisible box that surrounds the shape. You draw the biggest shape that fits in the box. All measurements are in cm.

In my language, the position numbers tell you where the top left corner of the bounding box is. The first number is the distance to go along the top of the page from the top left corner. The second number is the distance to go down from that point. The top left corner of the bounding box in the above instruction is 3cm along the page and 6cm down.

The final two numbers give the size of the bounding box. The first number is its width. The second number is its height. For a rectangle, if the two numbers are the same it means draw a square. If they are different it will be a rectangle (a squashed square!)

Here is a program representation of my Mondrian-inspired picture.

1. Rectangle(Black, 0, 0, 1, 15)
2. Rectangle(Black, 1, 0, 14, 1)
3. Rectangle(Black, 15, 0,1, 15)
4. Rectangle(Black, 9, 1, 1, 14)
5. Rectangle(Black, 1, 5, 14, 1)
6. Rectangle(Black, 3, 6, 1, 9)
7. Rectangle(Black, 6, 6, 1, 4)
8. Rectangle(Black, 12, 6, 1, 6)
9. Rectangle(Black, 1, 8, 2, 1)
10. Rectangle(Black, 13, 9, 2, 1)
11. Rectangle(Black, 4, 10, 5, 1)
12. Rectangle(Black, 10, 12, 5, 1)
13. Rectangle(Black, 0, 15, 16, 1)

14. Rectangle(Blue, 1, 1, 8, 4)
15. Rectangle(Red, 7, 6, 2, 4)
16. Rectangle(Red, 10, 13, 5, 2)
17. Rectangle(Yellow, 13, 6, 2, 3)
18. Rectangle(Yellow, 1, 9, 2, 6)
19. Rectangle(White, 10, 1, 5, 4)
20. Rectangle(White, 1, 6, 2, 2)
21. Rectangle(White, 4, 6, 2, 4)
22. Rectangle(White, 10, 6, 2, 6)
23. Rectangle(White, 13, 10, 2, 2)
24. Rectangle(White, 4, 11, 5, 4)

Create your own copy of my picture by following these instructions on squared paper. Then create your own picture and write instructions of it for others to follow to recreate it exactly.


<to be continued>