All these images were created with IFS Construction Kit. Click on an image for a larger view. Click on the corresponding ifs file to view the functions systems, or download the file so you can open it in IFS Construction Kit.


Sierpinski
Sierpinski converging to his triangle
Durer
Durer's Pentagons
Spleenworth Fern
Barnsley's Spleenworth Fern
 

Examples from Gerald Edgar, Measure, Topology, and Fractal Geometry, Springer-Verlag, 1990. [ifs file]
Heighway
Heighway Dragon
Twin Dragon
Twin Dragon
Levy Dragon
Levy Dragon
Pentigree
McWorter's Pentigree Dragon
Pentadentrite
Pentadentrite
Eisenstein
Eisenstein Fractions
Barnsley's Wreath
Barnsley's Wreath
Koch Snowflake
Koch Snowflake
 

Examples from Kevin Lee and Yosef Cohen, Fractal Attraction: A Fractal Design System for the Macintosh, Academic Press, 1991. [ifs file]
Eiffel Tower
Eiffel Tower
Nautilus
Nautilus
Spiral 1
Spiral 1
Spiral 3
Spiral 3
Square Snowflake
Square Snowflake
Starfish
Starfish
 

Examples of tilings from "Fractal Tilings in the Plane," Richard Darst, Judith Palagallo, and Thomas Price, Mathematics Magazine, Vol. 71, No. 1, February 1998, 12-23. [ifs file]
Horizontal Tiling
Horizontal Tiling
Terdragon
Terdragon Tiling
Gosper Snowflake
Gosper Snowflake Tiling
4 rep tile
4-rep Tile
4-rep tile with symmetry
4-rep Tile with Symmetry
5-rep tile with symmetry
5-rep Tile with Symmetry
 

Examples from "Number Systems With a Complex Base: A Fractal Tool for Teaching Topology," Daniel Goffinet, American Mathematical Monthly, Vol. 98, No. 3 (March 1991), 249-255. [ifs file]
b = -0.62e^(2pi/7)
b = −0.62e2π/7
b = -0.697e^(2pi/5)
b = −0.697e2π/5
b = 0.2 + 0.6i
b = 0.2+0.6i 
b = 0.5 + 0.5i
b = 0.5 + 0.5i 
b = 0.8 + 0.2i
b = 0.8 + 0.2i
b = 0.65 - 0.3i
b = 0.65 − 0.3i
 

Examples of Triangle Fractals motivated by Fractal World by Dave Ryan (website no longer available) [ifs file]
Sierpinski Triangle
Sierpinski Triangle
3 row triangle fractal
3 row triangle Triangle
Two rotations
3 row fractal with rotations
4 row triangle fractal
4 row triangle fractal
Reflective Symmetry
2 rows with reflective symmetry
Reflective Symmetry
Opposite reflective symmetry
 

Examples from Paul Bourke's website on fractals and chaos [ifs file]
Chaos
Chaos
leaf
Leaf
Maple leaf
Maple Leaf
spiral
Spiral
Mandelbrot
Mandelbrot like
Tree2
Tree
Tree3
Tree
 
 

Examples of color stealing
 
Heighway input image
Input Image
Heighway IFS
Heighway Dragon
Snowflake input image
Input Image
snowflake IFS
Snowflake
Fern input image
Input Image
Fern IFS
Fern
Spiral input image
Input Image
Spiral IFS
Spiral
Koch snowflake image
Input Image
Koch Snowflake
Koch Snowflake
 

Examples of fractal ferns from Ferns of the Canberra Region, a website maintained by David Nicholls and Christopher Nicholls. [ifs file]
Barnsley's fern (modified pinnae)
Barnsley's Fern (modified pinnae)
Culcita (=Calochlaenia) dubia
Culcita (=Calochlaenia) dubia Fern
Fishbone fern
"Fishbone" Fern
Cyclosorusfern fern
Cyclosorus Fern
 

Examples of Pythagorean Trees
45 degrees
45 degrees
60 degrees
60 degrees
Pythagorus as a tree
Pythagorus as a 45 degree tree!
10 degreees
The tips of a 10 degree tree
 

Examples of Koch Curves with n-gons [ifs file]
(4,1/3)-Koch curve
(4,1/3)-Koch Curve
(7,0.15)-Koch curve
(7,0.15)-Koch Curve
(7,1/5)-Koch curve
(7,0.20)-Koch Curve
(10,1/5)-Koch curve
(10,1/5)-Koch Curve
 

Examples of Fractal Movies. Click on an image to start the movie. All of these were constructed using the Fractal Movie Creator in IFS Construction Kit.
Heighway to Sierpinski Triangle
Heighway Dragon to Sierpinski Triangle
Dancing Heighway Dragon
Dancing Heighway Dragon
Sierpinski to fern
Sierpinski Triangle to Fern
Dancing Sierpinski
Dancing Sierpinski
Starfish
Rotating Starfish
 

Examples of Symmetric Fractals using a single affine transformation or a given IFS, then modified using a cyclic or dihedral symmetry group. For an explanation of how these were created, see the Help section. [IFS file]
McWorterZ5-sm
Z5 Symmetry
KochD2-sm
Koch curve using D4 symmetry group
hexagonZ6-smStained Glass Window (with Z6 Symmetry) HeighwayZ2-smHeighway Dragon using Z2 symmetry group

The following examples are from Symmetry in Chaos: A Search for Pattern in Mathematics, Art and Nature byMichael Field and Martin Golubitsky, Oxford University Press (Edition 1, 1992/95) and SIAM (Edition 2, 2009) [IFS file]
astigmatismD4-sm
Astigmatism (D4)
cashmireZ50-sm
Cashmire (Z50)
catherineWheelZ9-sm
Catherine Wheel (Z9)
doilyD8-sm
Doily (D8)
fiftynations-sm
Fifty Nations (Z50)
pentagonZ5-sm
Sierpinski Pentagon (Z5)
snowflakeD6-sm
Snowflake (D6)