I have long been fascinated by number sequences and finding the patterns within them. This brings me to a fun topic . . . Fractals!
What are Fractals? – According to the Fractal Foundation, a fractal is a never-ending pattern that repeats itself at different scales. This property is call “Self-Similarity”. This means that as you look closer and closer into the details of a fractal, you can see a replica of the whole. What you may not know is that fractals of been of interest to people for over 2,000 years when Euclid, a Greek mathematician, claimed a straight line segment can be prolonged indefinitely . . . although, Mandelbrot stated the new fractal geometry is different . . . Oh, those crazy mathematicians! (But, now I’m starting to sound like an episode of The Big Bang Theory . . . so, so I’ll move on)
Frankly, I think it’s easier to understand fractals by seeing an example.
Step 1 – Take Triangle
Step 2 – Subdivide by three
Step 3 – Subdivide again by three
Step 4 and beyond – Keep subdividing by three
This can literally go on and on
Let’s see with a simple line
We can do this with a number of elements
Okay, so this is possible in graphics, but you may be wondering . . .
Are there naturally occurring fractals? – You may not know it, but we’re surrounded by fractals every day. From the veins in a leaf, to the branches on a tree, the structure of a snowflake, mountain ranges, rivers, lightning bolts, and much more. We can’t go a day without fractals. Below are a few examples of naturally occurring fractals.
As a design approach, fractals can be very inspirational and there are some easy on-line resources for generating your own fractals
Illuminations – http://illuminations.nctm.org/ActivityDetail.aspx?ID=17
Easy Fractal Generator – http://www.easyfractalgenerator.com/
Just looking at fractals can be inspirational and there are on-line galleries and other resources available for viewing
Fantastic Fractals – http://www.fantastic-fractals.com/index.html
Fractal Foundation –http://fractalfoundation.org/
Even googling the word “fractal” will generate many examples. Enjoy exploring fractals and discover ways to use them as inspiration.
Update . . .
Here are a couple of simple fractal-like drafts . . . a sis-shaft Bronson lace and a 16-shaft summer & winter