2024 Joint Mathematics Meetings
Steve Butler
Artists
Steve Butler
Morrill Professor
Iowa State University
Ames, IA, USA
Statement
The "headlight" LEGO piece is able to be used to allow connections coming off the sides. By combining many such pieces together it becomes possible to form fractals, particularly ones which work well with right angles. So by combining many such pieces of this type together (only one type of LEGO brick, with two different colors) we have constructed a Menger sponge intersected with a cuboctahedron. This is able to see both the familiar Menger sponge structure, but thanks to the slicing off of the eight corners also is able to show how the Koch snowflake shows up inside the Menger sponge.
Artworks
A Menger sponge is a 3D fractal formed by starting with a cube and then drilling out the "middle-third" on each face, and then repeating this action again, and again, and .... This is a variation on a level-two Menger sponge (meaning two iterations of the drilling have been done) which has also had its corners cut off. This illustrates different viewpoints on the Menger sponge and shows the emergence of some 2D fractals in the cross sections. For emphasis, the cut-off corners are highlighted in orange. We also note that removing the corners leaves a cuboctahedron, and this is the largest cuboctahedron made from the single type of LEGO brick known as "headlight".
Constructed at the Iowa State University mathematics REU in Summer 2023.