Algorithmic Sketch BookJoshua Graf 587672Studio Air

Vase Variations

This was a particularly interesing variant that i found occuring as I changed the step on one of my sliders

Step = 0

Step = 8

WK 1

TO explain my low-res image, I set up 9 series’ and fed 3 of each into a construct point tool. For the z coordinate of each however, I first fed the series through a x^2 function. I decided to do this to try and get a curve. Having created these point I then used them in the Create Circle from 3 Points tool, giving me a variety of circles which I then fed into a loft command. Initially I just wanted to see what i could create purely from Grasshopper, but as I experimented with the sliders more and more I discovered that they could create seemless shapes quite easily and so stuck with it to create my variety of ‘vases’.

SeriesConstruct Point

x^2 functionCreate Circle

Loft

WK 2

Here in my trialling of surface division I played around with what elements I could relate to points and some different arrangements of that

WK 3

This was an initial trial after the demonstration was given in class

Playing with rotation values

This one was cool because the small branches zoomed in on became fractal.

In this one I reset the start curves hexagonally to to and recreate a snow flake

These 2 were varieties of this manor of generation

This one still had the six arms but I rotated their initial starting positions 3 dimensionally. The top image is the TOP view and the bottom is a perspective of the generated form

These two were alot more effort to create. It uses the same princi-ple as the Anemone L Systems but applied to a 3D tube. The first one is the basic tree, and the second one applies a relative down scale of the tube radius as well. It really looks like sprotuing flowers which is interesting.

WK 4

Experimentation taken from class, with a form being created by dividing surfaces of a pyramid over 6 iterations. The above has new surfaces x0.3 of the original, the below has x0.8.

The recorded iterations beneath the x0.8 model

1

2

3

4

5

6

Same process applied to a triangulated NURBS surface

My first attempt at applying the same process to spheres, but instead with the new speheres sprouting from the top and bottom. The left is without recorded data, the second is.

This one is the same but with the smaller spheres only being reproduced at a x0.3 scale. It was another fun example where the pattern would continue even as you zoomed in.

I then attempted to set it up so that each successive sphere would create new spheres on 6 of the vertices. My inital attempts (left) produced some very unexpected results, but I eventually got it to work.

WK 5

A documentation of the evolutuion of a pyramid using the surface splitting recursion algorithim.

Base

Initial Run

Loop 1

Loop 2

Loop 3

Loop 4

Loop 5

Loop 3

Loop 5

The change in form and size as the midpoint extrusion length is adjusted. The smaller ones are cleaner and intersect less.

0.1

0.3

0.5

0.7

0.9

Pattern of 0.1 vs 0.9

Evolution applied to a triangulated cylinder

Base0

12

3 4

This iteration showed how there can potentially be an effective limit to the extent on which the algorithm is useful. Anything past the 4th iteration on this particular shape proved to be (1) difficult to comprehend (2) very difficult for th computer to process.

I created a column with varying triangle sizes to see the effect on the duplication.

I created a rather interesting array of views, both inside and outside the shape. The changing/morphing surface also added depth.

I then, rather accidentally at first, began affect the way in which the normal vectors were formed. These images demonstrate a switching of this vector direction of internal to external each loop.

3 loops

8 Loops