Definition of fractal, from Hyperdictionary:
A fractal is a rough or fragmented geometric shape that can be
subdivided in parts, each of which is (at least approximately) a
smaller copy of the whole. Fractals are generally self-similar (bits
look like the whole) and independent of scale (they look similar, no
matter how close you zoom in)
Good brands are fractal. Every interaction you have reflects the interaction you’ll have with every other piece of the whole, as well as the whole itself. Since "brand" is shorthand for the total experience you get from buying, using, servicing, and disposing of a product, creating a great brand requires taking a fractal point of view to the process of designing total experiences where everything — large and small — is consistent and mutually self-reinforcing.
What’s the implication for creating cool stuff? I haven’t fully thought this one out, but I think it all boils down to leadership. Behind every great product is someone who had a vision of the end thing in mind and was able to say "yes" and "no" to help the development team understand that vision. In a way, great products require a kind of fractal leadership able to recognize the right texture for a button, the right message for the box, the right approach to customer support and service.