Fractals are situations where the geometry seems best approximated by an infinitely "branching" sequence - used, for example, in modeling trees. For work on fractals that I have done as a theoretician, I recommend the included links.
I just happen to have an original answer, and I want to make it known.
Fractals
Fractals
Nobody. Fractals are not owned by anyone!
But to a mathematician, it is a neat, neat subject area. Why are fractals important? Fractals help us study and understand important scientific concepts, such as the way bacteria grow, patterns in freezing water (snowflakes) and brain waves, for example. Their formulas have made possible many scientific breakthroughs.
Complex mathmatic equations.
By their very nature fractals are infinite in extent.
Fractals that which includes the fourth dimension and with which we can identify that our body's veins and nature are self similar.
Fractals
Fractals
If you look closely and carefully enough, nature is ALL fractals; snowflakes, leaves, tree branches, coastlines, everywhere.
Fractals are real mathematical patterns that repeat at different scales. They manifest in nature through shapes like ferns, clouds, and coastlines, where similar patterns are seen at both small and large scales.
Benoit B. Mandelbrot has written: 'Gaussian self-affinity and fractals' -- subject- s -: Electronic noise, Fractals, Multifractals 'The - Mis - Behavior of Markets' 'The fractal geometry of nature' -- subject- s -: Geometry, Mathematical models, Fractals, Stochastic processes 'Fractals' -- subject- s -: Geometry, Mathematical models, Fractals, Stochastic processes
Fractals are commonly used for digitally modeling irregular patterns and structures in nature. They are also very useful for image compression, producing an enlarged picture with no pixilation.
Fractals are patterns that are found in nature frequently. Many of them are based off of the golden ratio or Fibonacci's sequence.
Crystals are usually not fractals.
Pi is a number. There are no fractals of pi.
Nobody. Fractals are not owned by anyone!