Kig (software)

Inside the figure

Another object is available inside Kig, it is a Python language script. It can accept Kig objects as variables, and always return one object.

For example, if there is already a numeric object inside the figure, for example 3, the following Python object can yield its square (9):

def square(arg1):
    return DoubleObject(arg1.value() ** 2)

The variables are always called arg1, arg2 etc. in the order they are clicked upon. Here there is only one variable arg1 and its numerical value is obtained with arg1.value().

If no one wants to implement the square of a complex number (represented by a point in the Argand diagram), the object which has to be selected at the creation of the script must necessarily be a point, and the script is

def csquare(arg1):
    x = arg1.coordinate().x
    y = arg1.coordinate().y
    z = x * x - y * y
    y = 2 * x * y
    x = z
    return Point(Coordinate(x, y))

The abscissa of the point representing the square of the complex number is ${\displaystyle x^{2}-y^{2}}$ as can be seen by expanding ${\displaystyle (x+iy)^{2}=x^{2}-y^{2}+i(2xy)}$, Coordinate(x,y) creates a Python list made of the two coordinates of the new point. And Point creates the point which coordinates are precisely given by this list.

But a Python object inside a figure can only create one object and for more complex figures one has to build the figure with a script:

Figure created by a script

Kig comes up with a little program (written in Python) called pykig.py which can

1. load a Python script, e.g. MyScript.py
2. build a Kig figure, described by this script
3. open Kig and display the figure.

For example, here is how a Sierpinski triangle can be made (as an IFS) with pykig:

from random import *
kigdocument.hideobjects()
A = Point(0, 2)
A.show()
B = Point(-2, -1)
B.show()
C = Point(2, -1)
C.show()
M = Point(.1, .1)
for i in range(1, 1000):
    d = randrange(3)
    if d == 0:
        s = Segment(A, M)
        M = s.midpoint()
    if d == 1:
        s = Segment(B, M)
        M = s.midpoint()
    if d == 2:
        s = Segment(C, M)
        M = s.midpoint()
    M.show()