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.

triangles_2015912_21111

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.

triangles_2015913_123115

The lines were not thick enough so added some strokeWeight and tried out QUAD_STRIP instead.
triangles_2015913_164228

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

triangles_2015913_1792

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.

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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.

triangles_2015914_16724

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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