What does it mean if a universe is shaped like a fractal?

Question

Wow awesome answers , thanks.

Answer 1

Nothing particularly special. Fractal geometry is simply a mathematical method of representing complex shapes.

However, perhaps this will help: One characteristic of a fractal is self-similarity. To say that the universe has a fractal character would imply that if you took one portion of it and magnified it and looked at it again, it would look similar to the original. If you then magnified it again it would still look similar.

In general, the universe does exhibit this behavior. Take all the regions of known space. In it you would find scatterings of dense regions and sparely populated regions. If you magnify that and look closer you would find galaxies, which contain areas of dense star clusters separated by more sparely populated regions. Magnify again and you would find within the clusters, even more clusters. Magnify again and you would find star and planetary systems, regions of dense matter separated by space. Magnify again and you might find yourself between grains of sand on a beach of one of the planets, areas of dense material separated by space.

You could keep that up even to the atomic level. So the fractal geometry does lend itself well to the description of the universe.

Another way to think about fractal geometry is that it gives mathematicians a way to deal with dimensions that are not whole numbers. We live in a three dimensional world, we work with 3, 2, and 1 dimensional objects. Fractal geometry allows us to describe things with a dimension of, say, 2.8 or 1.5.

Answer 2

Nothing because it isn't. A fractal is a drawing of the results of iterating a particular equation point by point. The different colors that are shown when they draw fractals a set by the value of the equation at that point. The universe doesn't have repetitive values and shapes. It would also mean that the universe would be disjointed. For example if it shaped like a star to get from one pint to the next, you would have to navigate through the middle. There's no observation to support that.

Answer 3

dogsafire beat me to it, yes the universe is self similar as you look at it at different magnifications.

Trees are also fractal and self similar. If you cut a branch off of a tree and stick it in the ground, it tends to look like a smaller version of the bigger tree. The branches tend to split into the same number of groups and at the same angles, each branch is just a scaled down representation of the parent tree. Gravity and weather account for variations in the tree's shape at different branch levels.

Answer 4

It means that Mandelbrot was right ☺

Doug