Steps to Infinity (1994)

The steps in this image come from a dragon curve, like the one seen on the poster for this event (and described in the notes for Fiery Dragon. Below, I show two different colourings for a dragon curve in the plane. The curve is made up of smaller and smaller copies of itself, as the colourings indicate.

There are two transformations which define the dragon curve each small dragon seen above can be described by a sequence of these two transformations. To create the steps, I've assigned a unique height to each small dragon. Below, I show the steps inside a white sphere, which represents the sky. It doesn't look much like a very believable sky here, but I'll fix that. The lighting I've used here is much simpler than in the final image and it shows.

If you look carefully at Steps to Infinity, you will notice (part of) a Mandelbrot set in the sky, amongst the clouds. I began with a portion of the Mandelbrot set, shown below. It may be familiar to you from Ken Musgrave's image on the cover of the 1994/95 Fractals Calendar. In this case, I've changed to colours more appropriate for a blue sky.

For the next step, I've mapped the square image onto the inside of a white sphere, which will represent the dome of the sky in the model of my scene. Notice that this image is considerably lighter than the first, and this is due only to the white colour of the original sphere.

I create some clouds for the sky by using a fractal texture function which selects blues and whites for each pixel based on something called fractional Brownian motion.

When the clouds are combined with the Mandelbrot set image, the final Mandelbrot sky image comes to life.

And the final image once again...

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