# Project 05: Curves

In this composition I wanted to simulate a biological object that has weight. Using iterative curves for the form, I created a 3D texture reminiscent of a red blood cell.

Professors Roger Dannenberg & Golan Levin • Fall 2015

In this composition I wanted to simulate a biological object that has weight. Using iterative curves for the form, I created a 3D texture reminiscent of a red blood cell.

To be fair I didn’t really follow the instructions for the assignment because I didn’t study a curve and use a formula to replicate it. Instead I played around with a recursion example we looked at in class to see what kind of forms I could generate from animating nested ellipses. I think the result is pretty–I especially like the way that the layers of transparency distort the colors to create what look like afterimages–though the amount of user interaction is minimal.

For this project, I wanted to use fairly simple original curves and interactions to create many different and interesting patterns. After looking through many distinct curves, I finally decided on using cycloid curves just because I think it will be more challenging to generate very complex shapes. The first problem I encountered was drawing the curve with small rectangles. For some reason, it just didn’t draw in the right way but now I obviously got that fixed. Then I just started playing with the curves, changing some index numbers or flipping the curves to try to make the generated shaped more interesting.

sketch

57 out of 74 students completed Project 05, the *Composition with Curves*. Broadly speaking, we’re very pleased with the results of your creative research. The results are lovely, intriguing and surprisingly personal. Many of you dove right in to MathWorld and explored some really interesting and challenging territory, despite having (in some cases) limited background in mathematics. Nice work!

*Of the students who presented Projects, the average grade was 2.37, with a standard deviation of 0.36. Below are some of our favorites.*

One of the most intriguing, unusual and well-engineered projects was this one by Aman Tiwari. Aman sought to simulate a Harmonograph, a device which creates a drawing by moving a pen with multiple pendulums. For context, here’s a video showing a Harmonograph in action:

Aman’s project has lots of great coding patterns worth studying, such as smoothing of the control signals, and dynamic adjustment of the simulation timestep to accomodate performance on different CPUs.

This outstanding composition by Lexi Yan, exploring Daisy spirals, is a gorgeous design with a supple interaction and a delicious surface.

John Sprong’s investigation of the Spirograph curves produced this lovely composition, which has an absolutely luscious surface and a liquid-feeling interaction. There’s really careful craft here, and he learned a lot, too.

This design by Sydney Ayers, which uses a grid of astroid curves, is simply killer. It has carefully chosen colors, an enjoyable interaction, and a really interesting flipping between positive and negative forms.

Another appealing project using the astroid curve is this one, by Edward Shin. The relationship between the mouse interaction and the movements of the shapes is puzzling and fun.

Alex Reed was one of perhaps another five or six students in the class who investigated the astroid curve produced from the envelope of a series of ellipses; his design had a mind-bending interaction, and a lively animated quality produced by the addition of some subtle randomness. Zai Aliyu is another student who explored this curve to good effect; her design has the timeless qualities of a good logo.

That said: why did so many of you explore this one particular shape? MathWorld has *hundreds* of curves….

In addition to the above, we’d also like to shout-out additional thanks to David Frank, Marantha Dawkins, Hannah Levesque, Rachel Baker, and Maggie Mertz for their especially innovative and lovely submissions for Project 05.

I really enjoyed creating this project, however,not being a math major or anything of the sort, I will admit that this project did initially throw up some walls for me in terms of translating curves to logic then logic to syntax. I now will have an easier time with this and liked playing with all the final design aspect. Enjoy.

For the ‘curves’ project, I started my piece based on what we learned this week with adding points when the mouse is clicked and then manipulating them over time (exaggerating the line in shape and size). I added the function of ‘curveTightness’ so that the shape also changes by constricting and expanding depending on the position of the mouse, and inserted “if” statements to change the color as well.

Ok. I really liked the astroid shape. But it seemed really boring to create the shape only by calculating x and y with the formulas they gave on the website. Instead, I was inspired by our midterm exam-the second question created a curve much like one of the four sides of an atroid curve, the only difference is that it is created by iterative yet variable lines-could I make the curve by overlapping other shapes in succession? Doing so would give me an easier way to animate the curve.

I originally wanted to make a quadrifolium….but I wanted to make a curve with curves-aka, an astroid made of ellipses!

(Based on where your mouse is, the size and proportion of the astroid will change. Based on where you click, the mouse will change colors!)

(um…I fell asleep. Will using one of my free late days excuse the tardiness?)

http://mathworld.wolfram.com/AstroidRadialCurve.html

This project was surprisingly very difficult, seeing that we as we needed to use alot of calculus and I haven’t been in touch with my mathematical side in a while. I mostly experimented with what the professor gave us in the examples, and surprisingly the shape turned out pretty interesting.

I wanted to explore density in objects something I am very interested in physical objects. So it was natural for me to try and interact with this idea in a digital form. I’ve never thought of computer generated images such as the one I have created as being physically dense ( as in more than just weight) but this particular shape sort of draws that potential out for me. The way this shape interacts with the plane and the mouse and the viewer creates an interesting dialogue between user and computer, as the more you try to increase the density of the object the more your computer fails to respond as quickly as it normally would. For me the most interesting parts of the code come from when the mouse is nearest to the top part of the screen.

Sorry for the lack of comments life is catching up to me.

I used the hatch function I made from a prior project and wrote a series of additional algorithms that use it to draw generative sketches from a vectorized probability field.

This program allows you to see generalized higher order forms that you may not normally see. Think of it as a crystal ball, made with code.