She is also the treasurer of the Adult Numeracy Network. Note: Sarah Lonberg-Lew is a math teacher and professional developer in Gloucester, MA. In attendance: Sophie, Lynda, Jeniah, Eric, Patricia, Amy, Nadia, Mark, Usha, Audrey, Maggie, Kevin List of applications of Voronoi patterns in different fields: Voronoi patterns superimposed on a melon: For lots more information, including applications beyond what we talked about at the meeting, google “Voronoi.” Here are a few more links that I found interesting:Īrticle with some interesting variations: We had a lot of fun exploring Voronoi patterns and ended the meeting with people feeling like they wanted to keep exploring. They made predictions about what would happen before placing each seed. Jeniah, Maggie, Sophie, and Mark started by investigating the Voronoi game and used their exploration to come up with theories about how the pattern is generated from the seeds. ![]() (Side note: Annotating on a giraffe is my favorite thing that I have seen happen over Zoom.) They later moved on to annotating directly on a giraffe (!) and asking the (still open) question of how to locate the seeds if they are not in the picture. Patricia, Eric, and Audrey used annotation to explore the relationships between lines between seeds and lines connecting seeds. Each group also explored specific questions that arose during their play. With only the instruction to play and have fun, we broke into groups for the next hour, using a communal Jamboard to record some of our work.Īll the groups explored the rules for the pattern by playing with placing seeds, noticing relationships, and trying to predict the results of placing new seeds. I also provided a link to a document with some push and support cards (note that there wasn’t a specific task, but the support cards are around figuring out the rules for the pattern). This website has a game based on the Voronoi pattern: This website offers an interactive element where you can click to place seeds and generate your own Voronoi pattern: I wonder what the rule is behind this pattern.Īfter a solid round of noticing and wondering, I shared that this pattern is called a Voronoi pattern and that the dots are called “seeds.” I shared a couple resources before letting people loose to play in breakout rooms.I wonder if it is possible for more than three colors to come together at a point.I wonder why the dot is where it is in each shape.I wonder how you figure out how to place the dots.I wonder what the deal is with the dots.I wonder if this is connected to where post offices or fire stations should be.I notice that there tends to be only three colors touching at an intersection.I notice that there is folding symmetry with the dots between adjacent shapes.I notice that it looks like county seats.I notice that all of the polygons are irregular (the sides and angles are not the same).I notice that the dots are sometimes on the edge and sometimes closer to the middle of their own shape.I notice that the dots are not placed randomly.I notice that it feels like a map coloring problem.I notice that it feels like there are some reflections going on.I notice that there are not very many triangles, but lots of shapes with 4, 5, or 6 sides.In the context of noticing and wondering, these are some of the ideas the group came up with: I then revealed that the pattern in all four pictures is the same kind of pattern generated by following certain rules and shared another example of the same kind of pattern generated by a computer: Even though there is irregularity in the patterns, the shapes seem to have some uniformity of size.The shapes in the patterns mostly seem to have four, five, or six sides.All the pictures have a pattern involving shapes.The turtle picture has several patterns in it, not just on the turtle.The honeycomb pattern looks more three-dimensional than the other patterns.In the leaf, the borders are a similar color to the shapes, but in the other pictures they are not.The turtle is the only one under water. ![]()
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