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Logo design project

Feb 13, 2025

For a college design class, I was asked to create two logos. I decided to create a logo for EcoSim and Appleseed Robotics. EcoSim is the simulator I maintain for farming and forestry robots. Appleseed Robotics is the (provisional) name for the Farm Robotics Challenge team that I’m on at CMU.

Parametric curves

For EcoSim’s logo, I wanted something that combined themes of the natural world and modeling/simulation. At first I thought of pixel art of leaves or flowers, but that was a little on the nose. I also thought about depicting a line plot of, say, a topographical map or some signal plot that was made to look like mountains. Finally, I thought of something I learned in high school math class: Simple math equations that could be tuned to look like flowers. These are parametric equations.

Rose curve

The formula for the rose curve is simple and beautiful:

r=a⋅sin⁡(b⋅θ)0≤θ<c⋅2πr = a \cdot \sin(b \cdot \theta) \\ 0 \le \theta < c \cdot 2\pi

Of course, the radius and angle for a polar curve can be converted to Cartesian coordinates like:

x=r∗sin⁡(θ)y=r⋅sin⁡(θ)x = r * \sin(\theta) \\ y = r \cdot \sin(\theta)

Water lily

This is a curve that I found on Matthias Wandel’s website. Here’s the formula:

r=(d+sin⁡(b∗θ))ϕ=θ−cos⁡(θ∗e)/fx=r∗sin⁡(ϕ)y=r⋅sin⁡(ϕ)r = (d + \sin(b * \theta)) \\ \phi = \theta - \cos(\theta * e) / f \\ x = r * \sin(\phi) \\ y = r \cdot \sin(\phi) \\

Mystery flower

This is a parametric equation that I found here, though I wasn’t able to find the true source. Its formula is:

x=a⋅sin⁡(g⋅θ)1+cos⁡2(h⋅θ)y=a⋅cos⁡(h⋅θ)sin⁡4(h⋅θ)x = a \cdot \frac{\sin(g \cdot \theta)}{1+ \cos^2(h \cdot \theta)} \\ y = a \cdot \cos(h \cdot \theta) \sin^4(h \cdot \theta)

We can then rotate this primitive nn times by the angle 2π/n2\pi / n. Note that aa just fixes the size of the flower.

Earlier concepts

Some early sketches for EcoSim logos

Some early sketches for Appleseed Robotics logos

Finished logos

I wanted EcoSim’s wordmark to be neutral: not playful, not too stylized. I wanted it to convey modernity (no serifs) without being futuristic in a corny way (no fonts mimicking seven-segment displays or Atari games).

For Appleseed, I went with Costa, a font that’s subtely playful.

Finished logos for both EcoSim and Appleseed Labs. EcoSim is an abstract star or flower, orange and yellow. Appleseed's is a robot with a red apple head.

Other notes

The live demos above were written in p5.js. The finished logos were made with Adobe Illustrator.