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 converging to his triangle |
![]() Durer's Pentagons |
![]() Barnsley's Spleenworth Fern |
Examples from Gerald Edgar, Measure, Topology, and Fractal Geometry, Springer-Verlag, 1990. [ifs file]
![]() Heighway Dragon |
![]() Twin Dragon |
![]() Levy Dragon |
![]() McWorter's Pentigree Dragon |
![]() Pentadentrite |
![]() Eisenstein Fractions |
![]() Barnsley's Wreath |
![]() 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 |
![]() Nautilus |
![]() Spiral 1 |
![]() Spiral 3 |
![]() Square Snowflake |
![]() 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 |
![]() Terdragon Tiling |
![]() Gosper Snowflake Tiling |
![]() 4-rep Tile |
![]() 4-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 = −0.62e2π/7 |
![]() b = −0.697e2π/5 |
![]() b = 0.2+0.6i |
![]() b = 0.5 + 0.5i |
![]() b = 0.8 + 0.2i |
![]() b = 0.65 − 0.3i |
Examples of Triangle Fractals motivated by Fractal World by Dave Ryan (website no longer available) [ifs file]
![]() Sierpinski Triangle |
![]() 3 row triangle Triangle |
![]() 3 row fractal with rotations |
![]() 4 row triangle fractal |
![]() 2 rows with reflective symmetry |
![]() Opposite reflective symmetry |
Examples from Paul Bourke's website on fractals and chaos [ifs file]
![]() Chaos |
![]() Leaf |
![]() Maple Leaf |
![]() Spiral |
![]() Mandelbrot like |
![]() Tree |
![]() Tree |
Examples of color stealing
![]() Input Image |
![]() Heighway Dragon |
![]() Input Image |
![]() Snowflake |
![]() Input Image |
![]() Fern |
![]() Input Image |
![]() Spiral |
![]() Input Image |
![]() 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) |
![]() Culcita (=Calochlaenia) dubia Fern |
![]() "Fishbone" Fern |
![]() Cyclosorus Fern |
Examples of Pythagorean Trees
![]() 45 degrees |
![]() 60 degrees |
![]() Pythagorus as a 45 degree tree! |
![]() The tips of a 10 degree tree |
Examples of Koch Curves with n-gons [ifs file]
![]() (4,1/3)-Koch Curve |
![]() (7,0.15)-Koch Curve |
![]() (7,0.20)-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 Dragon to Sierpinski Triangle |
![]() Dancing Heighway Dragon |
![]() Sierpinski Triangle to Fern |
![]() Dancing Sierpinski |
![]() 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]
![]() Z5 Symmetry |
![]() Koch curve using D4 symmetry group |
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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]
![]() Astigmatism (D4) |
![]() Cashmire (Z50) |
![]() Catherine Wheel (Z9) |
![]() Doily (D8) |
![]() Fifty Nations (Z50) |
![]() Sierpinski Pentagon (Z5) |
![]() Snowflake (D6) |