I have been studying the Super Ellipse for a project and come across the work of Reza Ali. Have a look at his work…nice tool to explore super-formulas. enjoy>
From the artist: Reza Ali
I have been playing around with the superformula for a week or two now and I am totally addicted to created different shapes, forms, lines, and designs using this formula. Initially I developed a 2D application to explore the formula, but now I have extended it to 3D with a couple more rendering/texturing options to help highlight the aesthetic that can be rendered from this formula. The 3D application is minimal and fun to play with, download it here, or see more images after the link.
From the creator of 2D SuperShapes – Reza Ali comes the 3D version of the same, a visual exploration into superformula. Besides the ability to play with parameters and explore transformations, included also are rendering/texturing options to explore possible aesthetic that can be generated from the formula.
For more information:
You can download the application here for Mac, Windows and Linux or See more Renders. The application that can be used to create these shapes and render an image of them at a super high resolution (5333×2100).