Photo contest week #27 - "Patterns of nature".

_{Snapped using Nokia C30, Edited in PhotoStudio app, leaf placed on a paper}

Patterns of Nature: Fractals

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fractals
Fractal is one of the many amazing designs that can be seen woven in the fabric of nature. In this contest, I will be presenting the fractal design found on many plant leaves.

The word fractal has its roots from Latin suggesting that the design is based on repeated fractures breaking. This design can be seen in the way the veins on this leaf continuously breaks down smaller veins for transporting water and other minerals throughout the plant leaf.

_{This is my picture for the contest, no editing snapped with Nokia C30}

Many trees also have this design in the way it grows branches. It starts big and keeps getting smaller as you follow the branch.
This same design is also visible when lightning continuously breaks down into smaller branches as it sweeps across the sky.

Zooming closer to the leaf will give a clearer picture of this design.

_{leaf zoom and snapped with Nokia C30 to make fractals veins more visible}

The mathematics in the design
A fractal formula was first formulated in 1978 by Robert W. Brooks and Peter Matelski in their Kleinian groups study. Two years later, Benoît Mandelbrot mathematically simulated the fractal formula which we now know as the Mandelbrot set.

_{The formula for Mandelbrot set. Designed in Photostudio app}

Where

C and Z are complex numbers.
n is zero or a positive integer.

Starting with Z = 0,
C is in the Mandelbrot set if the absolute value of Z_n never becomes larger than a certain number (that number depends on C ), no matter how large n gets

_Wikipedia

The visual Pattern it created was beautifully represented as a complex structure that kept repeating itself so that each new version was smaller than the previous.

_{Mandelbrot set from Pixabay}

Conclusion
Mathematics is a type of poetry written with numbers that creates Pattern and those who easily identify this Pattern are the ones who fall in love with mathematics and the designs in nature built on real formulas.

I am inviting @mahadisalim, @shahariar1 and @mhizta to participate in this exercise.

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