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Home > Tutorials > What are Fractals? > Fractals Lesson Plan > What are fractals?

What are fractals?

PowerPoint of fractal images


Fractals are shapes that can be split into many parts, and each part will look approximately like the whole thing.


Some fractals can be made by hand. For example the Koch Curve is an example of a simple fractal that can be drawn by hand, (at least up to 3 iterations)

Koch Curve Animation

Individual images

This animation was created using a Java applet http://www.arcytech.org/java/fractals/koch.shtml


Fractals in Nature

As well as drawing fractals you can grow them!


Romanesco broccoli fractals. Photograph taken August 21, 2004 with a Canon D60 camera and Canon 28-135mm lenses.
This is a public domain photo from PDphoto.org


Walker, J. (2005). Fractal food: Self-similarity on the supermarket shelf. http://www.fourmilab.ch/images/Romanesco/ Retrieved May 30, 2011.
This document and all images and programs included herein are in the public domain.


SWITZERLAND from space

Walker, J. (1998). Switzerland from Space. Retrieved from http://www.fourmilab.ch/images/suisse_espace/ May 30, 2011.


Glue fractal



Center 36

György Kepes, Lichtenberg Figure: A. R. von Hippel, 1951, photographic enlargement on fiberboard panel. Courtesy of the Department of Special Collections, Stanford University

A photographic panel created by the artist, designer, and visual theorist György Kepes (1906 –2001) depicts a fractal-like burst of electricity exploding across the picture plane. The fantastical image is otherworldly, even supernatural. Kepes discovered the pattern— called a Lichtenberg figure after the eighteenth-century scientist who first created such images— in the laboratory of physicist Arthur R. von Hippel at the Massachusetts Institute of Technology (MIT).


Nature is full of fractals (PowerPoint) 12.37 MB

Fractals from space (PowerPoint) 22.39 MB

Guess What (PowerPoint) 11 MB

Fractals in you







Fractal Tree


The most famous fractal is the Mandelbrot set we will be creating our own Mandelbrot fractals in the lab.

The Mandelbrot Set


The mandelbrot set is way to complex to draw by hand. The only way to create an mandelbrot set is to use a computer program. The program that we will be using is called Ultra Fractal.

You can download version 2.04 and install it at home if you wish. I have also created a set of notes that explain how to install and use Ultra Fractal 2.04.



APA citation:
Russell, R. (2023, February 06, 10:05 am). Fractals Lesson Plan
     Retrieved May 19, 2024, from

Last refreshed: May 19 2024. 11:22.40 am

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