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Painting With Math

In honor of Earth Day, today I’m going to show you how to create this abstract painting of a snail in a garden using nothing but math—and the computer takes care of all the math, so really, ANYONE can do it. Read on to learn how and try it for yourself!

Note: this post is image-heavy and may load slowly on poor internet connections.

What you need:

  • An image editing program like Photoshop, ProCreate, or the GIMP. I used ProCreate, and Photoshop has the most similar blend modes which take care of the math for us. The GIMP is free but doesn’t have the same blend modes, though I’ll try to list alternates.
  • The images provided in each step of this tutorial

General Instructions

I’m assuming you have basic familiarity with using an image editing program. If you don’t, poke around a bit, or read a getting started tutorial for your chosen program, them come back here.

To download each image, right-click and choose save as, then save it to your hard drive. Then you can insert it into your working file in your graphics program.

Alternately, you can simply right-click, choose copy, and then paste it directly onto a new layer in your working document.

Instructions for each step are provided underneath the image required for that step. Images that are provided for reference, but not used in the working file, are labeled *reference image* underneath. And for those interested in the actual math, equations are included in a separate section at the end!

Let’s get started!

Insert this image on a new layer, leave the blend mode on normal.
Insert this image on a new layer, set blend mode to Luminosity (Value in GIMP) at 100% opacity
*reference image*
It should look something like this.
Insert this image on a new layer, set blend mode to Lighten at 100% opacity
*reference image*
It should look something like this.
Insert this image on a new layer, set blend mode to Overlay at 91% opacity
*reference image*
It should look something like this.
Insert this image on a new layer, set blend mode to Multiply at 100% opacity
*reference image*
It should look something like this.
Insert this image on a new layer, set blend mode to Difference at 100% opacity
*reference image*
It should look something like this.
Insert this image on a new layer, set blend mode to Lighten at 100% opacity
*final image*
Your final image should look something like this.

Final Instructions

Now that you have your finished image, try experimenting with different blend modes for different layers and see what happens. You may like a different effect better!

You can also try adding additional layers of noise, or even photos from your camera roll, and changing their blend modes to build up even more depth to the image and discover interesting new effects.

Here’s mine:

I added some more noise and blended it using non-GIMP available blend modes (Lighter Color, Pin Light)

The Math

Here are the equations for the blending operations used in this tutorial. PLEASE NOTE these are all based on my own understanding and experimentations, and are not authorized, endorsed, etc. by ProCreate, Photoshop, or the GIMP. Any mistakes are my own, and I’m sure there ARE mistakes—math isn’t my forte, I just find blending operations interesting and enjoy trying to figure it out.

Also note some of these are more descriptions than actual equations; again, math isn’t my forte.

In the equations, A refers to the Active layer being used to blend, and B refers to the target layer or layers the blending is being applied to.

In order of appearance:

  • Luminosity: preserves the Luminosity (aka value) of A and blends the hue and saturation with B
  • Lighten: max(B,A) –uses individual RGB channels for the calculations
  • Overlay: (A>0.5)*(1-((1-2(B-0.5))*(1-A))) + (A<= 0.5)*(A*2B)
  • Multiply: A*B
  • Difference: 1-abs(B-A) such that black is not inverted, white is always inverted, all other colors invert based on the brightness of the composite channel, and similar colors cancel to black
Published inArtIllustrated

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