# Barnsley fern

## Primary tabs

Major Section:
Reference
Type of Math Object:
Example

## Mathematics Subject Classification

28A80 Fractals

### What's with the fern?

Interesting post. It could be made more interesting by providing some background: for example: Are there similar results for other coefficient values? How would one go about proving this result? Who discovered this and in what context?

### Re: What's with the fern?

I think this field has its roots in the 19th century. Of course, Mandelbrot first popularized fractals. Michael Barnsley is the man behind fractals generated by iterated function systems. He has a textbook _Fractals Everywhere_. He used the technique to implement an image compression scheme in which only the coefficients of the transformations are stored. This is treated in his book _Fractal Image Compression_. The hard part is finding the coefficients that will yield a given image.

### Re: What's with the fern?

Fascinating. I have a different question: are things like the Mandlebrot set "self-similar fractals" with this definition? If so, can the contractions be written down?

### Re: What's with the fern?

No, Mandelbrot is not this kind of fractal!

### Re: What's with the fern?

I think some questions are answered in the parent object.