Mathematterfly Genesis

I like illustrations, particularly pen and ink with watercolor wash. Today for Thing-A-Day I wanted to create a faux plate one might find in a book illustrating various species.

Mathematterfly Genesis

Mathematterfly Genesis

The inspiration for this piece came from a book I bought a few months ago titled: “Computers and the Imagination, visual adventures beyond the edge“. This book focuses on some of the beauty in mathematical equations. This butterfly is a computer generated shape of a butterfly using the equation listed under DNA Sequence.

Buterfly equation

Butterfly equation

This piece meets a few objectives I set for today. Instead of using watercolor crayons with the pieces last week, I bought some tubes of watercolor paint. I wanted to experiment with mixing and blending colors. It is harder than it looks. I feel these came out too muddy looking. It is going to take much more practice to get to a point where I would like to be in this medium. Another goal was to use the LaTeX formatting I installed last night. I was able to format the equation used in this piece. I also wanted to create a program using the equation to create this image. I used the Processing language to generate the image.

Mathmaterflys - (c) 2010 Vince Thompson

Inspired by the book "Computers and the Imagination, visual adventures
 beyond the edge" by Clifford A. Pickover Chapter 3 Butterfly Curves

int winX = 1024;
int winY = 768;
int halfWinX;
int halfWinY;

void setup()
 size(winX, winY);
 halfWinX = winX/2;
 halfWinY = winY/2;

void draw()
 float pi_100 = 100 * PI;
 float prevXX = 0;
 float prevYY = 0;

 for(float theta=0; theta<pi_100; theta += 0.010)
 float r = exp(cos(theta)) - 2*cos(4*theta) + pow(sin(theta/12),5);
 float x = r * cos(theta);
 float y = r * sin(theta);
 float xx = (x * 90) + halfWinX;
 float yy = (y * 90) + halfWinY;
 if(theta > 0)
 line(prevXX, prevYY, xx, yy);
 prevXX = xx;
 prevYY = yy;
 print("theta: " + theta + ", cos(theta): " + cos(theta) + ", exp(cos(theta)): " + exp(cos(theta)) + ", x: " + xx + ", y: " + yy + " ");

The piece uses a combination of tools. Processing to program the image. KSnapshot was used to grab the Processing image. Gimp was used to crop and adjust the image. OpenOffice was used to create the document and placeholder for the image. This combination was printed onto watercolor paper and received a watercolor wash.

ā€“ About SomeoneKnows ā€“
(c) 2010 Vince Thompson


One Response

  1. Wow am I impressed! I have a degree in mathematics and am always looking for ways to combine math concepts with my paintings but I have never done anything approaching this level of sophistication.

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