# Patterns and Symmetry By [Madhav Goyal](https://paragraph.com/@madhavg) · 2021-12-18 --- When we observe regularity  in anything it pleasures us and helps us comprehend the nature of reality. Patterns are beautiful either in equations or Nature it makes us fell everything is in control and follows a certain framework  Recognizing symmetry and relations between different ideas leads to understanding  the world. In Math and Physics symmetry and patterns show up in places which we might have thought of as random.  Observing Patterns are one of the most delightful activities to Mathematicians and indeed mathematics can be seen as the search for regularities, and the output of any function is a mathematical pattern .There are numerous objects that show remarkable patterns and symmetries which are beyond Human limits some are within our limits and shatter all our expectations like The Mandelbrot set When you zoom at the outer rims of the figure you never see the same pattern which means it never repeats itself no matter for how much time you try you will never encounter the same pattern in which lies the beauty of it. It lies in the complex plane, which means it doesn't  exist in reality but just in our ideas. Its made by just one equation x^2 + c where c is a complex number in the complex plane . It seems really crazy to me that you can get a never ending patter from just one expression. It was named after Benoit Mandelbrot a mathematician who saw its first visualization. Talking about patterns there is a sequence which is quite remarkable-  Fibonacci numbers is a sequence of numbers which is one of the most intriguing and just seems to show up everywhere. It’s a sequence of numbers starting from zero in which the next number is formed by Adding the last two .Its as simple as that. They appear in branching of trees, arrangement of leaves on the stem ,flowering of plants and many biological systems which I don’t know the reason of , maybe plants like attracting Math lovers or themselves are Mathematician. It has been observed that the possible no. Of ancestors on the Human chromosome X also follow the sequence of the Fibonacci Numbers . They just don’t only show up in Biological systems but also in optics .When Light is refracted ,the no of different beam paths have k reflections where k>1 where k is a Fibonacci number. Its use is ubiquitous in Math and physics.   And as I was talking about patterns and relations between different concepts there also exists a relation between the Mandelbrot set and the Fibonacci numbers. The number of branches that come of the tendrils of the hyperbolic part of the Mandelbrot set happens to come in Fibonacci sequence. This seems weird to me because the Mandelbrot set is present in the complex plane and Fibonacci numbers are present in real which quite shows the elegance of it. Symmetry is aesthetically pleasing and attracts our attention but there's something more symmetry than just its beauty, Symmetries form the basis of our reality . Symmetry simply means the invariance when we rotate or fold something .   Symmetry principles play an important role with respect to the laws of nature. They summarize the regularities of the laws that are independent of the specific dynamics. Founding of invariance in wave function while interchange of two particles led to discovery of new particles called Boson and the ones that show variance are called Fermions. Elementary particles  gain masses due to the gauge theory which I just read about and is intimidating so I wont be mentioning it anymore. Pattern recognition plays a key role in finding cycles of weather and storms, migration of birds and  one of the most -important dividing time in blocks . As our ancestors learned that Sun rises daily after a particular period and the period varied a little in different season they realized that it was a cycle and happen again and again till eternity which lead to systematic quantization of time .   All that I have talked about now seems okay and a bit cool But when I read Love and Math by Edward Frenkel I fell in love With Patterns and started to see the world through a different preceptive and finding joy and beauty in everything . This seems a bit fake or philosophic as this is just being written by me and these are my thoughts biased towards somethings and preferring one thing over the other but this defines who I truly am But no one can stress enough on the presence of patterns in our lives and what we can learn from them become something more than ourselves . I might not have been “converted to Math” as Edward Frenkel would say But he has taught me to find the joy even in the deepest of Concepts which would I  have not been able to without him and Grant Sanderson. Both of their work have affected me a lot and changed my feelings towards Math and its beauty.  P.S I am not very good At Math so my description might have fault and I you found them Dear Reader email me at- madhavgoyal007@pm.me and I would correct them. This is the longest one I have ever written Hope you like it. --- *Originally published on [Madhav Goyal](https://paragraph.com/@madhavg/patterns-and-symmetry)*