#spiral

A spiral is a curve that begins at a central point and continuously moves outward, either getting larger (in an outward spiral) or smaller (in an inward spiral). It often revolves around a central point or axis. Spirals are fascinating because they appear in many aspects of nature, mathematics, and art. In this drawing exercise, I utilized several commands to draw such a system. However, this drawing is not a curved spiral but rather a segmented one. In this basic…

“In the heart of a sunflower’s embrace, its seeds weave a poetic tale—a dance of two spirals, parastichies they’re called. One unfurls gracefully from the center in the hush of clockwise whispers, while its counterpart whispers secrets in the tender breaths of counterclockwise motion. A subtle ballet unfolds, where the number of these spirals gracefully mirrors the whispers of adjacent Fibonacci numbers, composing a delicate symphony in the sun-kissed fields.” says ChatGPT if I force it to be a little…

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…

As studied earlier in Grasshopper here, the sunflower spiral, or Phyllotaxis, or Fibonacci’s spiral, could be drawn as an exercise of looping in Rhino Python. Phyllotaxis is the arrangement or patterning of leaves, flowers, or other plant parts around a stem or axis. Thus, it refers to the specific geometric arrangement of these structures in plants. The term “phyllotaxis” comes from the Greek words “phyllon” (meaning “leaf”) and “taxis” (meaning “arrangement” or “order”). Phyllotaxis can vary widely among different plant…

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…

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…

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 (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…