1. VART3227
Evolutionary Graphics
Class 02: Coordinates & geometry

2. VART3227
Remember in last week. We described our patterns.
Horizontal lines distributed evenly…
Four squares, symmetric…

3. VART3227
Any systematic way to describe, notate, analyze visual
forms in everyday life?

4. Euclid

5. Euclidean Geometry
Greek mathematician – Euclid (300 BC)
Elements – first systematic text on the studies of
geometry. Assuming a small set of axioms
(assumptions), it proves other propositions by logical
deduction.
We focus on the Plane Geometry (2D)

6. Straight line

7. Circle

8. Parallel lines

9. Numbers
We also learn numbers in primary school.
Integer
Rational number
Real number

10. Integer
We are familiar with Integers,
1, 2, 3, 4, 5, …

11. Integer
Some number sequences are geometric in nature. For
example,
1, 4, 9, 16, 25, 36, …

12. Square number

13. Square number
In Context Free Art, we can have nested repetitions,
startshapemyShape
shape myShape {
loop 5 [y 1] {
loop 5 [x 1]
CIRCLE []
}
}

14. Integer
Another number sequence is,
1, 3, 6, 10, 15, 21, …
Guess what shape it is?

15. Integer
Another number sequence is,
1, 4, 9, 16, 25, 36, …
Can it be something else other than a square?

16. Integer
Hex numbers are,
1, 7, 19, 37, 61, …
It arranges like a hexagon.

17. Integer

18. Fibonacci numbers
One of the most interesting number sequence is the
Fibonacci number.
1, 1, 2, 3, 5, 8, 13, 21, 34, …

19. Golden section

20. Golden section

21. Typography

22. Golden section

23. Golden section
The ratio of the golden section is roughly,
1:1.618 or 0.618:1
If we take a look at the Fibonacci sequence,
1, 1, 2, 3, 5, 8, 13, 21, 34, …
When we divide two consecutive numbers …

24. Fibonacci number
Can you find the relation between the Fibonacci
numbers and this?

25. Coordinate system
Remember the 2D plane with X and Y axis.
It is a combination of geometry and the number system.

26. Coordinate geometry
y (+)
sin (θ)
angle θ
x (-)
centre (0, 0)
y (-)
cos (θ)
x (+)

27. Coordinate geometry
y (+)
x (-)
centre (0, 0)
y (-)
x (+)

28. Visual Design
Conceptual elements
Point
Line
Plane
Volume

29. Visual Design
Visual elements
Shape, e.g. SQUARE, TRIANGLE, SQUARE
Size
Colour, e.g. Hue, Saturation, Brightness
Texture

30. Visual Design
Repetition

31. Visual Design
Structure

32. Visual Design
Gradation

33. Visual Design
Radiation

34. CFA
Implementation in Context Free Art

35. Lines
Two points give you a straight line.
MOVETO (0, 0)
LINETO (1, 1)

36. Multiple lines
When you have multiple lines,
MOVETO (0, 0)
LINETO (1, 2)
LINETO (2, 0)
LINETO (0, 0)

37. Multiple lines
You expect a triangular shape?

38. Multiple lines
Take this one again,
MOVETO (0, 0)
LINETO (1, 2)
LINETO (2, 0)
LINETO (0, 0)
CLOSEPOLY ()

39. Shape
It looks better.

40. Circular path
Try the following circular path with ARCTO,
MOVETO (0, 0)
ARCTO (1, 0, 0.5)

41. Circular path

42. Circular path
Try the following circular path with ARCTO,
MOVETO (0, 0)
ARCTO (1, 0, 0.5, CF::ArcCW)
CF::ArcCW means clockwise.

43. Circular path

44. Circular path
To complete the path as a circle,
MOVETO (0, 0)
ARCTO (1, 0, 0.5)
ARCTO (0, 0, 0.5)
CLOSEPOLY ()
STROKE () []
FILL [h 60 sat 1 b 1]

45. Circular path

46. Circular path
To draw an ellipse,
MOVETO (0, 0)
ARCTO (1, 0, 0.5, 0.3, 180)
ARCTO (0, 0, 0.5, 0.3, 180)
CLOSEPOLY ()
STROKE () []
FILL [h 60 sat 1 b 1]

47. Circular path

48. Colour wheel – hue

49. Example photo

50. More path command
We start from a simple LINETO with the use of sine and
cosine functions we have learnt in secondary school.
LINETO (cos(?), sin(?))

51. Coordinate geometry
y (+)
sin (θ)
angle θ
x (-)
centre (0, 0)
y (-)
cos (θ)
x (+)

52. More path command
Let’s put it together.
MOVETO (1, 0)
LINETO (cos(30), sin(30))
STROKE () []

53. More path command
We do repetition within a path.
MOVETO (1, 0)
loop 2 [r 30] {
LINETO (cos(30), sin(30))
}
STROKE () []

54. More path command
We do more repetitions to form a polygon.
MOVETO (1, 0)
loop 12 [r 30] {
LINETO (cos(30), sin(30))
}
CLOSEPOLY ()
STROKE () []

55. More path command
We add a bit complication.
MOVETO (1, 0)
loop 12 [r (360/13)] {
LINETO (cos(360/13), sin(360/13)}
}
CLOSEPOLY ()
STROKE () []

56. More path command
We add a bit complication.
MOVETO (1, 0)
loop 12 [r (4*360/13)] {
LINETO (cos(4*360/13), sin(4*360/13))
}
CLOSEPOLY ()
STROKE () []

57. More path command
We fill it with colour.
MOVETO (1, 0)
loop 12 [r (4*360/13)] {
LINETO (cos(4*360/13), sin(4*360/13))
}
CLOSEPOLY ()
FILL () []

58. More path command
We modify the fill effect.
MOVETO (1, 0)
loop 12 [r (4*360/13)] {
LINETO (cos(4*360/13), sin(4*360/13))
}
CLOSEPOLY ()
FILL (CF::EvenOdd) []

59. Sample image

60. Randomness
We may from time to time to create something not that
deterministic. That is, we want surprise.
In mathematics, it is randomness and probability we
have learnt in secondary school.

61. Randomness
Consider throwing a coin, we have Head or Tail. If we
design a coin with one side red and other side blue, we
can draw the coin. It can either be red or blue.
By using Context Free Art, we achieve by using multiple
rules of the same name.

62. Randomness
First, we define a red coin,
path CoinRed {
MOVETO (0, 0)
ARCTO (1, 0, 0.5)
ARCTO (0, 0, 0.5)
STROKE () []
FILL [h 0 sat 1 b 1]
}

63. Randomness
Then we define a blue coin,
path CoinBlue {
MOVETO (0, 0)
ARCTO (1, 0, 0.5)
ARCTO (0, 0, 0.5)
STROKE () []
FILL [h 240 sat 1 b 1]
}

64. Randomness
Then we have two definitions of a shape,
shape MyCoin {
CoinRed []
}
shape MyCoin {
CoinBlue []
}

65. Randomness
You test by creating a repetition of the MyCoin rule.

66. Randomness
You can control the ‘randomness’ by specifying a number
for each rule with the same name.
shape myCoin
rule 10% {
…
}
rule 90% {
…
}

67. Exercise
Using a grid of 3 x 3 to design a few graphical patterns.

68. Exercise
Using a grid of 3 x 3 to design a few graphical patterns.

69. Exercise
Create a tile of the basic graphical patterns with the use
of randomness.