Tessalations and Transformations Inspired by Yayoi Kusama

I’ve been trying to use Processing to make something as close as I can to an image I saw on theartstack.com by Yoyoi Kusama called Infinity nets (Yellow, Black)

I came across the image when I was already trying out making a randomised net using beginShape(TRIANGLE_STRIP). My method creates an array of values for x, another for values of y that are in regular positions and then uses those to populate a 2D array of grid points (x,y) that has some randomised variation added. I feel that putting the points into a new array rather than making shapes from running through loops on x and y values allows me to do more than one thing with the same points. One thought I had was making some points brighter and bigger than others.

I have a number of images that I have made with the TRIANGLE_STRIP method that I will post separately, but I had reached this point when I found the Yoyoi Kusama image.


Changing the background colour to the yellow and lines to a very dark grey was a simple matter and with some changes of the numbers took me to this.


The lines were not thick enough so added some strokeWeight and tried out QUAD_STRIP instead.

Then put in some conditioning that said in some cases draw TRIANGLE_STRIP and in other cases QUAD_STRIP.


All of these efforts came out similar to the image, but were not quite right. I needed really to look more closely at the pattern. It looked to me that, although there was variation, predominantly I could see a pattern made up of diamonds/stars. I don’t have the vocabulary to describe properly. I mentioned what I have been up to in a telephone conversation with my aunt and she said that I was talking about tessalations and transformation. Tessalation is a whole new word for me and yet apparently it is something taught in GCSE maths. I know about repeat units and tiling and am aware of patterns, but this word tessalation has passed me by, so I need to do some more studying, I guess.

When I looked very closely, it seemed to me that the repeat unit (with some variation) was this.


It took an incredible length of time for me to really get the formula right to make a net with that repeat unit. When I have tidied up the code I will put it somewhere and link to it here. But this is the image.


You may also notice that previous images have a margin around the edge, but now I have opted for the pattern appearing to continue beyond the boundaries of the edge. Actually in all of the coding of these grids I have included a margin variable to give the option to change it and for the grid going past the edge of the display window I have simply chosen a negative value.

It is similar to the Yayoi Kusama image, but still not right. In my image each point either has 3 or 6 lines from it. Whilst the points have an irregularity in location, the repeat is consistently regular. Whereas the image I am trying to reproduce has some points which have 4 lines coming from them, some with 5, as well as a lot with 3 and 6. So as well as introducing some random variation to the location of the nodes from a perfect grid, I also need to add in some randomisation of the shape drawn. The quad strip has all points with 4 lines coming out of them, but I need to consider how to draw something with 5 lines coming out if it (and perhaps a fudge would be to erase one of 6 lines?).

In effect the aim is to introduce occasional defects to the regular pattern. To do this I need to first figure out the geometry and code for the defect then the trigger for it. As there will be 2 types of defect, I think switch() will come into play. Suggestions welcomed.

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