## Parametric Equations

Even though I’ve always had in mind to be an art director and illustrator, I’ve also been a bit of a math geek. In high school, one of my majors was math, studying Algebra, Geometry, Advanced Algebra, and Solid Geometry. I also belonged to the Math Club and the Calculus Club after school. In college I even took a year of Calculus even though I was getting a BFA in Advertising Design.

It did come in handy one year while working on my MA in Mass Communications and TV Production, I did some substitute teaching. During that time, a math teacher at Lincoln Park High quit in March to become a golf pro. I could only substitute 2 days a week and another guy could do 3 days a week, so between the two of us we took over the math classes teaching Algebra, Geometry, and Remedial Math until the end of the school year.

That’s the background behind my fascination with Fractals and Fibonacci Sequence in my posts a couple months ago. I investigated other mathematical terms at the time, but never posted the results of my exploration because of my busy work schedule. This post concentrates on Parametric Equations.

Last night I took a look at the results (back then using MJ5) and tried the prompts again last night with 5.2. Additionally, when the same two prompts were combined with the Style Raw and high stylize settings of 750 or 1000, suddenly the 2D results, created with stylize 50, became dimensional!

No I didn’t make up this first prompt on my own. I did choose “A highly detailed airbrush painting, using a parametric equation to create captivating art” as the subject, but the rest of the prompt was copying a formula found on line.

Prompt 1: A highly detailed airbrush painting, using a parametric equation to create captivating art, x(t) = A * cos(a * t) * cos(t) + A * sin(b * t) * cos(t) and y(t) = A * cos(a * t) * sin(t) + A * sin(b * t) * sin(t), where ‘A’, ‘a’, and ‘b’ are constants, and ‘t’ ranges from 0 to 2π. By experimenting with different values for ‘A’, ‘a’, and ‘b’, you can generate a variety of intriguing and visually appealing designs, combine this with other artistic elements and styles to create a captivating abstract design –ar 16:9

To see if the equation was actually effecting the image results, I then simplified the prompt.

Prompt 2: highly detailed airbrush painting using a parametric equation to create captivating art –ar 16:9 –s 50

The results were equally fascinating, with some differences without the equation.

Other mathematical terms explorations coming soon.