The Mandelbrot fractal is a very complex interactive pattern, discovered by Professor Mandelbrot. It is a form of Art which can exist in its complete, navigable form only on a computer.
You can calculate, draw or paint patterns which are parts of it, that's true, but it will function completely only if it is created on a computer and can be explored on the screen. It is created by means of a mathematical formula.
Once it has been created on a computer screen, you can click on any part of it. That part will enlarge, and show smaller details within it. You can then click on that small part, and zoom into an even smaller part. This process can be repeated many times. You discover that patterns repeat themselves but they mutate, that is, they change slightly.
It can also be used by specialists in various scientific and mathematical areas when they work with what is now called the geometry of chaos. As far as I understand it (and I do not really much of it at all!), it is said that some things which seem to be random, such as the movement and shape of clouds and the subtly different shapes of leaves on a tree, can be to some extent measured by the geometry of chaos.
When you zoom in, the patterns and shapes gradually change and mutate and look like all kinds of things you find the natural world: clouds, views from the air, trees, leaves, flowers, rivers, ferns, stalks, insects, creatures... whatever your imagination allows you to see! Although you are looking at something produced purely by computer mathematics, you are looking at fascinating art.
Different versions of the fractal will be in different sets of colours, depending on the software program you use.
You need to link to the right sort of computer program (unless you know someone who can write the program for you). There are several of these programs on the Internet. They might not run on your computer, or they might be difficult to handle. I have provided a link to one of them on my Useful Links page on this website. As far as I can see, it is reliable, but (if you are a school student) please check with your teacher before you link to it and start using it.
There is an image at the top of this page. I kept another image of the complete fractal, made by a program I found several years ago. I like this version because of its selection of colours. You can see it by clicking below. You cannot zoom into this picture, because it is only a graphic — it is not a working copy of the complete fractal:
Complete Mandelbrot fractal
I have selected some of the images I saved when I was zooming into the fractal. They are thousands and millions of times larger than what you see when you look at the whole fractal. Because they are so beautiful, I have processed some of them by erasing parts and making the background a different colour. You can see, for instance, one of the many spirals I found, and some of the shapes that look like weird insects. What they are is what you think they are.
They are here simply to inspire you to appreciate their intricacy and beauty and, I hope, to stimulate your imagination. I have kept them as small as possible so that they do not take too long to load. That means that the quality is not always perfect. These are only graphics, they are not navigable fractals, so you cannot zoom into them. Now, start clicking, and be amazed...
Mandelbrot pattern 1
Mandelbrot pattern 2
Mandelbrot pattern 3
Mandelbrot pattern 4
Mandelbrot pattern 5
Mandelbrot pattern 6
Mandelbrot pattern 7
Mandelbrot pattern 8
Mandelbrot pattern 9
Note: When you have had a good look at these pictures, go to the new section called Journey to Infinity: Fractal Thinking, to discover how you can use them for creative thinking!
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