Tetrahedral Helix and Snake Game
This is the Grasshopper definition that generates a tetrahedral helix (also called as Boerdijk-Coxeter helix) but in a funny way. This geometry is also a solution for tangent spheres. I generated the helix using Anemone components for recursion and gave it a little bit of responsiveness. I don’t know if it depends on the speed of your CPU but if it is slow enough, you’ll see the snake game of tetrahedral helix as it is driven by your input from a control knob. I’m not that interested in phone apps nowadays but this could easily be developed further as a real game :P
Here is the Grasshopper definition: (Requires Anemone Loop Components to be installed)
Cite this post
Related Posts
Spiral Staircase
April 17, 2023
This is a basic Grasshopper exercise, covering many fundamental topics. The aim is to create the parametric model of a spiral staircase. This is more educational than functional, I guess. Below is the explanation of the Grasshopper definition in three parts. Helix Points for the Spiral Staircase In the first part of the definition, I am defining the points ordered on a helix. First, I calculate the number of steps by dividing the total height value by the height of…
Spiral of Random
October 21, 2013
Grasshopper still surprises me. This definition draws a spiral by using a random component. It is obvious that the seed value of the random component has a relationship with an archimedean or a similar spiral. My intention was to create a definition to put a number of random points inside a circular area, not a rectangular one. While I grow the radius of a circle and get a t parameter evaluation from a random component using the same seed value…
Archimedean Spirals
December 17, 2012
In this exercise, Grasshopper draws various Archimedean spirals. It constructs polar points and maps them onto a range of angles and a number of points. The spiral’s turning speed is determined by the constant “a,” while the constant “n” gives unique names to the spirals by raising the angle variable to the power of 1/n. Wolfram Mathworld names the spiral with n = -2 as lituus, n = -1 as a hyperbolic spiral, n = 1 as a regular Archimedes…
Sunflower Spiral
December 22, 2011
Sunflower Spiral (or Phyllotaxis) can be constructed in Grasshopper according to Vogel’s model of parametric relationships. This model uses polar coordinates. The Grasshopper file is still working after more than 11 years -15.12.2022. This is such a powerful quality of Grasshopper, I think. It’s a good example of utilizing polar coordinates. It’s also fun to play with the parameters and constraints of the Sunflower Spiral. Also, there are very interesting results if you also connect the polar angle value to…
Dragon Curve Fractal
December 25, 2023
This week’s fractal is the famous Dragon Curve. Dragon Curve exhibits self-similarity, meaning parts of the curve resemble the overall shape, regardless of scale. It’s fascinating because a relatively simple construction process generates a complex and visually captivating fractal pattern. The Dragon Curve is often used to demonstrate fractal properties in mathematics and is popular in recreational mathematics due to its intricate and beautiful patterns. It has applications in computer graphics and is interesting in studying chaos theory, self-similarity, and…