Editing Fractal (section)

===Simulated fractals===
[[File:Julia-Set z2+c ani.gif|thumb|[[Fractal art]] made from a [[Julia set|Julia-Set]]]]
Fractal patterns have been modeled extensively, albeit within a range of scales rather than infinitely, owing to the practical limits of physical time and space. Models may simulate theoretical fractals or [[#fractals in nature|natural phenomena with fractal features]]. The outputs of the modelling process may be highly artistic renderings, outputs for investigation, or benchmarks for [[fractal analysis]]. Some specific applications of fractals to technology are listed [[#fractals in technology|elsewhere]]. Images and other outputs of modelling are normally referred to as being "fractals" even if they do not have strictly fractal characteristics, such as when it is possible to zoom into a region of the fractal image that does not exhibit any fractal properties. Also, these may include calculation or display [[Artifact (error)|artifacts]] which are not characteristics of true fractals.

Modeled fractals may be sounds,<ref name="music" /> digital images, electrochemical patterns, [[circadian rhythm]]s,<ref>{{Cite journal | last1=Fathallah-Shaykh | first1=Hassan M. | title=Fractal Dimension of the Drosophila Circadian Clock | doi=10.1142/S0218348X11005476 | journal=Fractals | volume=19 | issue=4 | pages=423–430 | year=2011 }}</ref> etc.
Fractal patterns have been reconstructed in physical 3-dimensional space<ref name="medicine" />{{rp|10}} and virtually, often called "[[in silico]]" modeling.<ref name="modeling vasculature" /> Models of fractals are generally created using [[fractal-generating software]] that implements techniques such as those outlined above.<ref name="vicsek" /><ref name="time series" /><ref name="medicine" /> As one illustration, trees, ferns, cells of the nervous system,<ref name="branching" /> blood and lung vasculature,<ref name="modeling vasculature">{{cite book |chapter=Fractal aspects of three-dimensional vascular constructive optimization 
| first1=Horst K. |last1=Hahn |first2=Manfred |last2=Georg |first3=Heinz-Otto |last3=Peitgen| editor1-last=Losa |editor1-first=Gabriele A. |editor2-last=Nonnenmacher |editor2-first=Theo F. | title=Fractals in biology and medicine | url=https://books.google.com/books?id=t9l9GdAt95gC | year=2005 | publisher=Springer | isbn=978-3-7643-7172-2 | pages=55–66 }}</ref> and other branching [[patterns in nature]] can be modeled on a computer by using recursive [[algorithm]]s and [[L-systems]] techniques.<ref name="branching" />

The recursive nature of some patterns is obvious in certain examples—a branch from a tree or a [[frond]] from a [[fern]] is a miniature replica of the whole: not identical, but similar in nature. Similarly, random fractals have been used to describe/create many highly irregular real-world objects, such as coastlines and mountains. A limitation of modeling fractals is that resemblance of a fractal model to a natural phenomenon does not prove that the phenomenon being modeled is formed by a process similar to the modeling algorithms.

{{anchor|fractals in nature}}