can be defined as "objects or figures which on magnification shows the original object or figure"
The nature has many fractals such as a fern leaf, path of a river etc.
Geometrical fractals includes a straight line, today's talk and much more!
The Koch Island is drawn by "copies of copies" method.
The base of Koch Island is a square as shown:
The motif of Koch Island is
The steps of making a Koch Island are as follows:
The figure after
So repeat it as much as you can!!!!
One exciting fact about the Koch Island is that it can tesselate a plane.
Tesselating a plane means that a plane can be covered up by infinite Koch Islands without overlapping or leaving spaces.
Question 1: Can anyone guess the area and perimeter of the Koch Island after n iterations?
Question 2: What is the minimun number of colors that you could use to color in your tessellation if no two adjoining Koch Islands are allowed to be the same color (no islands can touch even at 1 point)?
Question 3: What is the self-similarity dimension of Koch Island?
Question 4: Can you offer a MSW-Logo program to draw a Koch Island?