How Do You Construct an IFS for a Complex Fractal Pattern?

  • Thread starter Thread starter Deadstar
  • Start date Start date
  • Tags Tags
    Function System
Click For Summary
SUMMARY

The discussion focuses on constructing an Iterated Function System (IFS) for a complex fractal pattern within the unit square. Two methods are proposed: one involving crossed diagonal lines and the other utilizing a knots and crosses grid. The correct IFS equations derived include z/3, z/3 + 2/3, z/3 + 1/3 + i/3, z/3 + 2i/3, and z/3 + 2/3 + 2i/3, with a correction noted for the last equation. The conversation emphasizes the importance of understanding the transformation process in IFS rather than merely visualizing lines.

PREREQUISITES
  • Understanding of Iterated Function Systems (IFS)
  • Familiarity with complex numbers and their representation
  • Basic knowledge of fractal geometry
  • Experience with IFS software tools
NEXT STEPS
  • Explore advanced IFS techniques for fractal generation
  • Learn about the mathematical foundations of fractal geometry
  • Investigate the use of software like Fractint or Apophysis for fractal visualization
  • Study the implications of transformations in complex analysis
USEFUL FOR

Mathematicians, computer graphics developers, and anyone interested in fractal generation and IFS applications will benefit from this discussion.

Deadstar
Messages
99
Reaction score
0
Write down an IFS converging to the subset S of the unit square illustrated below.

[PLAIN]http://img707.imageshack.us/img707/2876/unledwcq.png

I have two ways I see this though.

First way is as a collection of crossed diagonal lines where at each iteration 5 new crosses are made.

2nd way is as a knots and crosses grid where at each iteration 5 new knots and crosses grids are created in the corners and centre of the old one (with the old one being deleted, although I think that's standard in IFS depending on the fractal...)

Which one, if any is correct?(also, I have this IFS software which I have just this minute figured out how it works so I'm testing a few things...)
 
Last edited by a moderator:
Physics news on Phys.org
Ok after a bit of playing around I get...

z/3,
z/3 + 2/3,
z/3 + 1/3 + i/3,
z/3 + 2i/3,
z/3 + 2i/3 + 2i/3

I think I've finally got the hang of this... It's more a shrinking of boxes than a drawing of lines...
 
Deadstar said:
Ok after a bit of playing around I get...

z/3,
z/3 + 2/3,
z/3 + 1/3 + i/3,
z/3 + 2i/3,
z/3 + 2i/3 + 2i/3

Sounds good, but you probably made a typo in the last equation, it should be z/3+2/3+2i/3
 

Similar threads

Replies
9
Views
4K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 2 ·
Replies
2
Views
9K
  • · Replies 30 ·
2
Replies
30
Views
5K
  • · Replies 2 ·
Replies
2
Views
3K
Replies
2
Views
3K
Replies
3
Views
2K
  • · Replies 49 ·
2
Replies
49
Views
8K
  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 4 ·
Replies
4
Views
3K