3. Computer Aided design¶
I was always interested in Mathematics although I didn.t and don´t understand the most of it. As a kid I was very bad in Math but when I started to work with CAD some things came back and I had to get into it again. Then there is this abstract thing about mathematics and geometries which attracts me the most. Like islamic Tiling, Penrose Tiling, Golden Ratio, M.C. Escher, Tessellations and the (possible) importance they play in nature.
Pythagoras Tree in Grasshopper¶
So I took the Phytagoras Tree, a fractal, and tried to make it in a parametrical model using grasshopper within Rhino 3D. So let me shortly explain what the Pythagoras Tree is. Have a look at the GIF.
It´s done very roughly in Paint.
If it´s done nicer it would look like this:
Guillaume Jacquenot Gjacquenot [CC BY-SA]
What´s important is the sequence of commands needed to make this tree as explained in the GIF… so you need to:
- copy the first square twice
- scale it down (Factor doesn´t matter)
- Move it on top of the first square
- And then rotate it…angle is not important
grasshopper¶
Now let´s go to Grasshopper. For those not familiar with grasshopper they can check it here. In short, Grasshopper is a visual programming language within Rhino 3D which uses containers in stead of scripts for parametric modelling.
Have a look at this short movie how I started to build the line of commands as described above.
What you see is that
- I drew a curve and connected it to a container in grasshopper
- looked for the endpoints as a reference where to move two copies of the curve
- made a ruler with 360 degrees. Doubled it and so doubled the curve. Make sure that the double rotation values are not the same but always 360 when added
- and then scaled the two curves down to factor 0,7
When all this is repeated on and on and some more rulers are added you get something like this. Notice that I also added some leaves to the Pythagoras Tree which have a random size to make it look more “natural”.