Geometry exploration

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Luke Messenger's picture
Submitted by Luke Messenger on Mon, 17/03/2014 - 12:58

This collection of shapes is the result of my learning the LOGO programming language.  

Sierpinski triangles interpretation

I wanted to create recursive or fractal patterns similar to the ferns already created, or other natural elements using mathematical formulae, eg. sunflowers using the Fibonacci sequence.  So first I tried creating the Sierpinksi triangles - triangles within triangles, each one a quarter the size of the next largest.  

This didn't really use any of LOGO's recursive ability, so I tried understanding how to make the code more condensed.

 

Defining new objects & metapatterns

The circle-like shape made of 36 repeated squares shows my understanding of how to define new objects in LOGO to use as shortcuts when creating an object which recurs.  

 
I created one version of this with 360 squares, each rotated one degree, which resulted in dense lines coming from the centre of the object.  Manipulating this version in a 3D space could result in metapatterns where lines crossed and created the illusion of circles within circles in aesthetically pleasing ways.
 
Recursive tree
 
Finally, the tree began as a 2D pattern, just using the commands left and right to create branches.  I spent some time playing branches but had a hard time understanding how the turtle returned on the lines which it had already created so as not to create a whole lot of scribble.  Inputting a single roll up function would mean when the turtle created a line, it would change orientation, then reverse, making mad spirals off into outer space, which was pretty cool, but looked like nothing.  I finally understood you needed to create one side branch, double the angle to the other side to create symmetry, then use the initial angle back to the centre to get the turtle to retrace its path.
 
 

 

Comments

Luke Messenger's picture

problems

Submitted by Luke Messenger on Mon, 17/03/2014 - 13:52.

Having some trouble inserting and viewing the world:  I'm hitting 'insert X3D world' after publishing and it doesn't come up with a preview.

Andy's picture

Reproduced with no problem....

Submitted by Andy on Mon, 17/03/2014 - 15:03.

I have taken your codes and reproduced the results with no problem. I have also published the x3d file (with viewpoint, background and navigation info checked) as Test.x3d into your folder so it is now loaded in your blog.

This could be a bug related to the inclusion of viewpoint, background and navigation info. I will need to investigate further.

Thanks for sharing the geometrical world you created. The 3D recursive tree is very cool. cool

 

Luke Messenger's picture

Thanks

Submitted by Luke Messenger on Mon, 17/03/2014 - 15:12.

Oh brilliant!  Thanks Andy.

Andy's picture

Formatting Logo programs

Submitted by Andy on Mon, 17/03/2014 - 15:25.

BTW, would you be able to format your Logo program to be syntax highlighted?

In this video http://www.youtube.com/watch?v=2eTATwBhsc0 at around 8:40 it shows you how to format Logo program in blog.

I also noticed your code about:

In the workshop I played for 100 repeat but why do you put 36 repeat?

Luke Messenger's picture

repeating

Submitted by Luke Messenger on Mon, 17/03/2014 - 17:15.

Originally I repeated 360 times with a one degree rotation just to create a circle, but changed it to 36 with a 10 degree rotation for computational simplicity.

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