As I have explained, the Ultrafractal mailing list leads to tweaking and other kinds of exchanges.
For example, Michèle Dessureault, who makes fractal formulas, among other things, periodically proposes a Cadavre exquis, in which she supplies the initial layer, and then anybody who wants to can add a layer. This will usually result in a tree of images, as people branch off the results made by others.
Mikko Vainiala proposed a collaborative exchange to construct a fractal in November, 2000. He would supply an initial layer, and his partner would supply a layer, and then he would supply another, and his partner would supply another, and so forth, until a satisfactory fractal had been constructed. Initially, he had two partners, and I was one of them. Each partnership constructed a separate fractal.
These are some of the versions that Mikko and I produced. The details of just exactly how we did this are somewhat fuzzy in my mind, but here is how it was to the best of my recollection.
Mikko originally sent me the black and white layer that is the first image in the gallery. I then sent back the second version, which has color in the layer, and Mikko said, "No, you have to give me a black and white layer, and when we have a satisfactory set of layers, we will add color." This business of working first in black and white was completely new to me, but I went along with it, and he took out the color, giving the version in image 3. Mikko then sent back a version which I haven't included in the gallery, adding slight color. For my next turn, I made the new texture much more pronounced. Mikko then added color and I added color. These are images four and five, respectively. I am especially fond of image five. Next, we started to play with the colors. The 8th image made me think of an alien astrolabe, with its shape and strange characters, so I gave it that name.
Image 9 is a version that Mikko came up with, to the best of my recollection. We didn't take it anywhere.
Images 10 and 11 were obtained by turning off some layers to look at others. Image 12 is the final version.
One of the really enjoyable parts of this project was the meanderings we both took off to the side, exploring alternate paths. We didn't just take the road less traveled by; we took them all.
Here is the gallery of images from this exchange.
You can find Mikko's fractal galleries here.