As my first week assignment, Dr. Schreck directed me to pick a fractal to study and write a brief recap of what I learned, and to find a 3D printable design of that fractal. I chose a design called the "dragon curve" or "Heighway dragon," and a vase created using that fractal that can be 3D printed.
The Fractalfoundation.org describes a fractal as "a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop." As such, fractals can be composed of very simple or very complex shapes, and explain more completely the surfaces of objects found in nature that don't fit easily into standard geometric shapes like cones, cylinders, cubes and spheres. Most spheres in nature aren't actually spheres, take the Earth for example. While it may look like a sphere, on close inspection its surface is made up of hills, valleys, mountains, flora and manmade structures.
The Dragon Curve was first investigated by NASA physicists John Heighway, Bruce Banks, and William Harter. It was described by Martin Gardner in his Scientific American column Mathematical Games in 1967. Beginning with a right angle, it can be described this way: starting from a base segment, replace each segment by 2 segments with a right angle and with a rotation of 45° alternatively to the right and to the left.
Here is an animation of the dragon curve in action, courtesy of wolfram.mathworld.com.
I chose the dragon curve because it has a shape that I believe will print well, while demonstrating a recognizable pattern when viewed from above. I don't completely understand how it forms at this point, but look forward to learning that in the weeks ahead. I believe the dragon curve vase will print well because of its gentle slope outwards, and tight corners. If the 3D printer's supporting material or scaffolding will need to hold up a shape that expands as it moves upward, better to have those slopes not be dramatic ones. I think that this will have very little in the way of supporting material, and thus be a better use of resources.
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design credit:Scott Rodgers
@scottyprogrammer on myminifactory.com https://www.myminifactory.com/users/Scottyprogrammer |
The Fractalfoundation.org describes a fractal as "a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop." As such, fractals can be composed of very simple or very complex shapes, and explain more completely the surfaces of objects found in nature that don't fit easily into standard geometric shapes like cones, cylinders, cubes and spheres. Most spheres in nature aren't actually spheres, take the Earth for example. While it may look like a sphere, on close inspection its surface is made up of hills, valleys, mountains, flora and manmade structures.
The Dragon Curve was first investigated by NASA physicists John Heighway, Bruce Banks, and William Harter. It was described by Martin Gardner in his Scientific American column Mathematical Games in 1967. Beginning with a right angle, it can be described this way: starting from a base segment, replace each segment by 2 segments with a right angle and with a rotation of 45° alternatively to the right and to the left.
Here is an animation of the dragon curve in action, courtesy of wolfram.mathworld.com.
I chose the dragon curve because it has a shape that I believe will print well, while demonstrating a recognizable pattern when viewed from above. I don't completely understand how it forms at this point, but look forward to learning that in the weeks ahead. I believe the dragon curve vase will print well because of its gentle slope outwards, and tight corners. If the 3D printer's supporting material or scaffolding will need to hold up a shape that expands as it moves upward, better to have those slopes not be dramatic ones. I think that this will have very little in the way of supporting material, and thus be a better use of resources.
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