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Math in Nature

This project attempts to explore the mathematical patterns in nature such as spirals, waves, flower patterns and recursive fractals using the mathematical formulas derived from these natural designs. But as things in natural are both symmetrical and assymmetrical but also random, the designs try to capture the same flows by keeping the projections random rather than very organized. There is also an attempt to move from monochrome patterns to colors again trying to capture the vibrancy of natural elements and between day and night.

produced by: Himani Kumar


The piece starts with more visible and discernable patternns that we observe daily like the trees on a windy night and star speckled skies or a sun travelling over a wavy ocean and makes a transition to more symmetrical patterns in nature that are small and require you to observe careful to admire its beauty. The project uses sin, cos and noise functions incorporated with the mathematical principles of patterns and fractals to create spirals, waves, trees and petal designs using 2 D primitives.

Concept and background research

I have felt a strong influence of natural patterns in some of the design work I have done in the past and nature inspired math has always interested me. I started with thinking of the patterns that I would like to create sketches for and then started to research about the design and the core mathematical formulas at the heart of those patterns. The theories that I selected were based on Recursive, Sin Waves, Fibonacci Spirals and Sinusoid patterns. I also decided early on not to borrow code from anyone's work but to code everything myself but I did take help and inspiration from a couple of resources in understanding the concept and the logic and then trying to code it in my way while also ensuring that my sketches did not end up being mere replicas but had an artistic expression of their own. Some of my sketches may seem a little rustic and rudimentary because of not borrowing more finessed code but I felt that it did go with the theme of natural patterns since they aren't perfect always and also because I could truly own this work.


The most challenging part of this project was to look at the patterns and break down the algorithm, especially the math for the algorithm. Although I had access to the basic formulas and tables researched but interpreting them into loops, variables, noise, sin and cos functions and determining the timing as well as the randomness in them were all small details that took me a lot of time to resolve for every sketch. I also chose a mathematical approach to the sketch to try and over come my fear of working with mathematical formulas, so this was also a personal journey of stepping outside my comfort zone technically.

Future development

Some of the natural progression of this idea could be to delve into more detailed patterns in nature or inspired by natures in 3D perspective, incorporating natural sounds would also enhance the experience greatly. With a little more time and experience I believe I could work on some very organic transitions for the scenes as well.

Self evaluation

While all the patterns had their own challenges, the waves were by far the most challenging for me and I felt that with a little more knowledge of some tools that I didn't possess at the time I could have made them more seamless and organic. Right now they seem a bit more on the abstract side. The fractal trees also took a lot of effort even though the math is simple but the logic to have the tree changes its shape, angle and branches with each sin wave movement was a very difficult vision to achieve. I spent the maximum time on the 2 above mentioned sketches. While for the waves I was able to achieve a transition from monochrome to color, the same I could not achieve for the trees as the results were not desirable at the time of this submission. But this is something I intend to work on as I am fascinated by Fractals of all kinds.


Reading Resources:

  •  The Nature of Code - Daniel Shiffman
  •   OfBook


Wave Math:

Fibonacci Spirals Math:

The Coding Train - Daniel Shiffman

        Flower pattern and math

        Fractal Tree math

*** Note: Watching the two challenges of the coding train along with the lecture on Algorithmic Thinking in the module helped me work on the approach to problem solving.