This post is going to be about a mathematical print titled IFS using CMM tile. The main design for this print is using a specific type of tile categorized as CMM. This tile is used as the basis to create the iterative function system (IFS) which was then printed. The alias I will be using is GMUMath401Student1. The purpose of this print is to fulfill an assignment of Math 401: Mathematics Through 3D Printing at George Mason University due September 28th, 2022.
IFS are a significant part of nature as they are in the structures of snowflakes to plants to shells. There are third main components to creating an iterative design they are scale, rotation, and translation. Scale pertains to how large the next iteration will be with respect to the previous one. If the value is greater then 1 then the iterations are increasing in size and if they were less than 1 then they are decreasing. With rotation, the iterations will be rotated the same degree with respect to the previous iterations. With translations there is a difference in that it just tells where the functions will be situated. In a 2D iterative function system, there will only be 2 dimensions for each component, while with 3D there will be 3.
In the pictures I have included, there is a table illustrating how this specific IFS was created. Since this is a 3D IFS, there will be 3 values in the scale, rotation, and translation columns. This system did not rotate so the values in that column were all 0s. The scaling was consistent for each dimension and function which were reduced by 40% with each iteration. The values in the translation column are where the functions will be placed at each of the triangles of the original tile. When I tried to use the original tile coordinates, I found that the first iteration was too small. So, I kept the translations coordinate the same but scaled the original tile by a factor of 2 so that now it would be twice as large. I found this would work by looking at the example code from class.
There was no need for any supports as the iterations were just stacked on top of the previous ones with no rotations. This print took a little less than 3 hours to print on the Ultimaker printer. We used a raft to make sure that the design didn’t move around while the layers were being printed. The print turned out well the first time. The pictures of the print, the code, STL, etc. are included. A website that helped me with my IFS design is cited below.

Classic Iterated Function Systems. (March 30, 2022). Retrieved September 25, 2022, from http://larryriddle.agnesscott.org/ifs/ifs.htm