I have more ideas for business and products than I have the time, energy or skills to pursue. I am throwing this one out there in the hope that someone else might run with it. You’re welcome.
Idea
1. You zoom into a region of the Mandelbrot set you like the look of. You have an the option to customize the colours.
2. You are shown a visualization of what this would look like on a shirt (front and rear).
3. If you like what you see, you click a button to order the shirt, choose your size and pay. It is then shipped to you.
Pricing
The fact you can design your own shirt and there is a vanishly small probability that anyone else will have the same design, means you can charge a big premium. Perhaps £50/$80 for a long sleeve shirt?
Feasibility
The software side of this business is fairly straightforward. After all the Madelbrot set is based on just z=z^2+c and you wouldn’t have to generate a high resolution image for the preview. But I know nothing about the clothing industry. I have no idea what it would cost to individually print a shirt or what printing technology you would use. Perhaps there are good economic reasons why no-one is already doing this (if they are, they aren’t very good at SEO).
I will be your first customer!
Successful Software 
That’s a nice idea.
a) Mandelbrot is boring. There are so many other nice fractals around.
b) Doing colors on fractals isn’t linear so that’s not as easy as it sounds.
c) The customer would need to use the fractal software. Not so easy, too.
d) The tshirt side seems to be covered well in the interwebs.
e) The fractal with the tshirt looks rather strange.
a) Boring? It’s infinitely complex (as far as I know)! But you offer other fractals, such as the Julia set.
b) You are just mapping numbers to colours. I don’t see how that can be very hard.
c) They just need to zoom/pan to a particular region of the Mandelbrot set.
d) I was thinking more of a party shirt (with a collar), not a t-shirt. Also most of the t-shirts are only partly covered in the Mandelbrot image. I was thinking 100% coverage.
:-)
a) Let me qualify: single fractals are boring. Usually, they are combined like in a tree. Check out http://www.uisoftware.com. Or my own site at http://www.beatrixwillius.de
b) It’s not linear like coloring an image with Photoshop. You can have multiple gradients and they may show up at different places.
c) okay
d) What’s a party shirt?
a) I prefer the ‘pure’ madelbrot set.
b) I’m sure there are lots of different ways to do it. Various standard mappings could be provided.
d) I mean a smart, long sleeve short with a collar. Not a t-shirt.
Have you checked ?
On their website they claim:
**Unique Fractal T-Shirt Designs**
Find Fractal T shirts for everyone (including yourself). Shop for popular Fractal designs in our marketplace, or **customize and personalize one yourself!** We have a huge selection of unique, Fractal tees (we’re talking about millions of cool-looking designs printed on T-shirts for women, men and children). With so many, it’s simple to find that one-of-a-kind tee that expresses your personality.”
Not affiliated with them in any way and cannot vouch for them, just found them via simple Yahoo! search for “personalized fractal shirt”.
URL?
Oops… sorry, wrote this in a hurry. Here is the URL:
http://www.cafepress.com/+fractal+t-shirts?utm_medium=cpc&utm_term=fractal%20t-shirts&utm_source=google&utm_campaign=entertainment%20apparel%20-%20us&utm_content=search-b
Happy New Year!
I couldn’t work out how you are supposed to choose your own custom design.