#DigitalGeometrySketchbook Days 21 to 30

Throughout the month of June 2021 I created a daily maths art piece, each one using different software or different techniques, as part of the #GeometrySketchbook challenge on Twitter. As mine was all digital artwork, I used the #DigitalGeometrySketchbook tag. Here are the results of days 21 to 30.

Any source code is offered as-is. Most of it was written in a bit of a hurry so it is likely to be messy and not as efficient as it could be. I’m just linking to it so that you can see how things were done, if you’re interested, and use it as a starting point for your own creations if you want to.

Feel free to ask if you have questions about any of the techniques I’ve used. And if you’re inspired by any of these pieces, do let me know. I’d love to see what else you come up with! You can tweet me at @SamHartburn or email

Days 1 to 10

Days 11 to 20

21 June

I’ve seen some beautiful watercolour maths art on Twitter, so I used Fresh Paint to add some colour to a seed of life (which was created in Geogebra). I could do with a lot more practice!

eed of life made of a central circle with 6 overlapping outer circles. Sections coloured and blended roughly, it all looks a bit clumsy. The colouring has gone outside the lines in some places, and the lines have bled into the colour.

22 June

I love optical illusions, so I used the NCTM Isometric Drawing Tool to create this impossible structure. The tool is easy to use – just select the shape you want and click where you want to add it.

Optical illusion formed by two adjoining triangles made of cubes.

23 June

I created these firey sine waves using the TikZ package in LaTeX, but after some cheeky modifications by @fionajw I just had to use Geogebra to turn them into singing fish.

Image is made from sine waves multiplied by integer values between negative ten and ten. The colour goes from yellow in the centre, through orange, to red at the peaks. The negative multiples mean that it has both horizontal and vertical symmetry.

24 June

I made this triskele in Efofex. It didn’t seem very well suited to this type of work, but does have lots of built in templates for standard text-book style diagrams, so it’ll come in useful for artwork briefs for work.

Circle with triskele design made of red, yellow and turquoise tear drop shapes spiralling round each other.

25 June

I made this image in Mathematica. It’s a sort of 3D seed of life, made using spheres instead of circles. You can see the code here. Mathematica is ridiculously powerful and I was hoping to find more time to play with it before my free trial expired, but sadly I didn’t.

Transparent spheres in bright colours overlapping each other.

26 June

This is one of my first attempts at ray tracing. It’s coded in ShaderToy, and I used this tutorial by Alan Wolfe. I enjoyed watching the image become more defined over time. The code for this image is here.

12 spheres in a circle, light coming from top, spheres ranges from very glossy to not at all glossy.

27 June

I made this with my son in Minecraft, using the Immersive Portal mod to make each hole lead back inside the cube. It also used the Pehkui mod to shrink the character so that it could go through one-block holes. We planned to make it work for all the holes, but it took too long! It was inspired by an impossible house that my son made. I tried not to be too offended when he laughed at my non-existent Minecraft skills.

28 June

Some time ago I wrote some Python modules to use for animating ruler and compass constructions. I dug those out to make this seed of life construction.

29 June

This is one of my favourite pieces from the month. I made it in, using a tutorial by George Francis. The code is here – press the Run button to generate a new image.

Teardrop shapes in gradients of red, blue, green and yellow, with randomly generated sizes and directions, in an approximate grid.

30 June

Day 30 was a bit of a cheat, I’m afraid – a compilation of the images from the previous 29 days. Although there is an image in the Day 30 space…

30 Maths Art images. The image for day 30 is a recursive image of all the images.





Leave a Reply

Your email address will not be published. Required fields are marked *

Hello! I’m Sam Hartburn, a freelance maths author, editor and animator. I also dabble in music and write mathematical songs. Get in touch by emailing or using any of the social media buttons above.

3D geometry animations cardioid constructions Geogebra GeogebraArt geometry MathArt mathober mathober2023 MathsArt OpenSCAD parametric parametric curves poetry polygons polyhedra ruler and compass Rupert polyhedra Sunday Animations