Creating fractals from nothing?

[Coolphreak]

For anyone here who is familiar with fractals and self similarity:

Is it possible to find local self similar patterns from a random arrangement of objects which can apply to the global arrangement of these objects?

For example, we have people walking in a city. The positions are somewhat random. Let's just pretend that everyone is still. If I "zoom in" and take a random sampling of the positions/arrangement of people w/in the local space I zoomed in on, is it possible to extrapolate this data to the more "global" space of people in the whole city using self similarity methods? Hopefully this is not too confusing

 

[neurocomp2003]

I doubt it, the rules to which selfsimilarity in the scope of this example IMO would be too complex for simple selfsimilarity as seen in most fractal systems.

If i recall, from one of the physics colloq I attended way back when...they studied fractal patterns of sand which may be the type of behaviours your looking to emulate with the above example but according to those researchers sand follows simple behaviour.

Then again if your just repeatedly zooming out, then everything is just dots =]

 

[tacman]

From my understanding, fractals are geometric patterns that repeat themselves on different scales, creating infinite complexity. They are often found in nature, such as in the branching of trees or the patterns of snowflakes.

To answer your question, yes, it is possible to find self-similar patterns in a random arrangement of objects. In fact, fractals are often created from seemingly chaotic systems. However, it is not a simple process and requires careful analysis and mathematical calculations.

In the example you provided, it is possible to find self-similar patterns in the arrangement of people in the city. By zooming in and analyzing a smaller portion of the city, you may find similar patterns in the distribution of people. This can then be applied to the larger scale of the entire city, using self-similarity methods.

However, it is important to note that fractals are not exact replicas of each other, but rather have a similar overall structure. So while you may find patterns in the distribution of people, they may not be identical to the larger scale. Additionally, the level of similarity may vary depending on the complexity of the system being analyzed.

In conclusion, it is possible to find self-similar patterns in a random arrangement of objects, including in the example of people in a city. However, it requires a careful analysis and understanding of fractal geometry and self-similarity methods.