Hofstadter Sequence.

Replies to This Discussion

Permalink Reply by David Rutten on March 31, 2013 at 3:09pm

The sequence formula

G(n) = n - G(G(n-1))

is not a formula that can be written in a Grasshopper Expression. You'll need some form of recursion or looping which in turn means you'll need a script component for this.

You'll also have to decide whether you want to just find a single number in the sequence (which will probably involve recursion and delegates) or whether you want to create the first N numbers of the sequence.

Attached is a sequence generator written in VB.

--

David Rutten

david@mcneel.com

Poprad, Slovakia

Attachments:

• HofstadterSequence.gh, 9 KB

Permalink Reply by David Rutten on March 31, 2013 at 3:14pm

If you can't open the file, here's a screenshot:

--

David Rutten

david@mcneel.com

Poprad, Slovakia

Permalink Reply by David Rutten on March 31, 2013 at 3:29pm

If you must use a GH Expression, this is the closest I could get:

--

David Rutten

david@mcneel.com

Poprad, Slovakia

Permalink Reply by Toussaint Jimenez Rojas on March 31, 2013 at 3:53pm

It's Weird the VB sequence have an error i dont know if the Expression its wrong but 

the Sequence have to be 

0 1 1 2 2 3 3 4 4 5 5 6 6......

And 

the Result of the script its 

0 1 1 2 3 3 4 4 5 6 6 6.......

the Number 2 and number 5 have to be twice in the Sequence and only appear just one time 

weird behavior 

Permalink Reply by David Rutten on March 31, 2013 at 3:57pm

http://en.wikipedia.org/wiki/Hofstadter_sequence#Hofstadter_G_sequence

--

David Rutten

david@mcneel.com

Poprad, Slovakia

Permalink Reply by Toussaint Jimenez Rojas on March 31, 2013 at 4:03pm

My mistake i'm wrong what i want to do its not Hofstadter Sequence. 

its Pair Sequence more simple 

:D 

Permalink Reply by David Rutten on March 31, 2013 at 4:07pm

Try the duplicate component.

--

David Rutten

david@mcneel.com

Poprad, Slovakia

Permalink Reply by newy011 on March 31, 2013 at 5:03pm

Or alternatively if you are using a c# or similar component you could use the following function to create the number sequence you need:

int numberFrequency = 2;

int myList = {};
for (int i = 0; i < 10; ++i)
{
     myList[i] = Ceiling(i / numberFrequency);
}

Notice that by changing the numberFrequency controls the number of repeating integers for a given sequence. 

Permalink Reply by Vicente Soler on March 31, 2013 at 5:45pm

In case he wants the code to work:

 

    int numberFrequency = 2;

    int[] myList = new int[10];

    for (int i = 0; i < 10; ++i)

    {

      myList[i] = (i + numberFrequency - 1) / numberFrequency;

    }

    A = myList;

If you prefer using Math.Ceiling replace the longest line with:

   myList[i] = (int) Math.Ceiling((double) i / numberFrequency);

But the duplicate component is faster and easier...

Permalink Reply by newy011 on March 31, 2013 at 6:13pm

Yes, my post (i thought) was quite obviously not presented in a format which was intended to be useable, but rather used to convey a simple/useful concept for repetitive number sequencing for future reference (i.e. not necessarily within the confines of GH). But thanks for idiot-proofing nonetheless.