e-sum
Art project to visualize complex exponential sums. Demo.
To create an interesting pattern, click "Create new Image" until you like it. It may take a few attempts before you stumble upon something pretty with intricate patterns.
I couldn't come up with better rules to generate nice looking patterns more consistently, so if you have suggestions - please let me know.
When you find something you like copy a link to the page - and share it :). A few examples that I found pretty:
What is going on here?
An exponential sum is the following expression:
When we translate it to complex plane we get both x and y coordinates:
x = cos(2 π f(x))
y = sin(2 π f(x))
Sequence of partial sums is plotted as sequence of connected points by this visualization.
Known issues
If you see your visualization "runs away" - likely you are running into floating point rounding errors.
To avoid the errors - reduce the Total steps value in the visualization settings, so that summation
stops earlier.
Build Setup
# install dependencies
npm install
# serve with hot reload at localhost:8080
npm run dev
# build for production with minification
npm run build
# build for production and view the bundle analyzer report
npm run build --reportThank you!
The project was inspired by a small conversation on Twitter.
If you liked it please let me know. Give it a star, or become a patron.
I hope you find it amusing :).
License
MIT
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