2009: Random-State Scrambler for Pyraminx

[Lucas]

With some help from Michael Gottlieb, I have developed a random-state scrambler for Pyraminx.
Here is a page with the scrambler, based on maintaining the old WCA format.

It does the following:

• Place a random edge at BL, ignoring centers (12 equal possibilities).
• Place a random edge at BR, ignoring centers (10 equal possibilities). This should probably be condensed with the last step some time, but it's not too costly to have them separate for now.
• Random L4E alg (96 equal equal possibilities) - list taken from Michael's index. This doesn't ignore centers, so it can be optimized even further.
• Randomly "AUF" each center piece and tip (3^8 equal possibilities).

Each of the 75582720 states is produced with equal probability, relying only on the PRNG for true randomness.
I would like to see it become the WCA scrambler for pyraminx, unless someone finally takes the initiative to write a small optimal solver that gives random scrambles and images.

[jbcm627]

Very nice.

How difficult would it be to add a scramble image (like this?)

[Lucas]

Very nice.

How difficult would it be to add a scramble image (like this?)

Here is a page with the scrambler, based on maintaining the old WCA format.

[jbcm627]

Here is a page with the scrambler, based on maintaining the old WCA format.

Ah whoops, missed that part...

[Ron]

Can anyone confirm that this is working correctly?
Then we can use it for WCA Regulations 2009.

Thanks,

Ron

[GunnarKrig]

Hi!

I already printed scrambles for this weekends competition. Does this mean I need to get new scrambles for some events for this weekends competition?

[Ron]

Does this mean I need to get new scrambles for some events for this weekends competition?

Yes, sorry.

[Lucas]

I see that this has been made official.

The first scrambler I posted does not work. This one averages about 17 moves. Today, I will try to post enough information to demonstrate that it generates a random state.

[Lucas]

Alright, I was going to do more, but I'll just post a simple explanation:
Here is a version of the official scrambler that lists the non-cancelled algs used to generate the scramble.

The scrambling method goes:

• Place two random edges at DL and DR (F2E, 120 cases)
• Permute the last four edges randomly (L4E, 96 cases)
• Randomly "AUF" each center and tip.

http://cube.garron.us/WCA/proposals/scramble/URSS_pyraminx_algs.htm gives a list of the algs used in each step, and what they do. As far as I have computed (and hand-checked some), the lists for both F2E and L4E should be complete and cover every case exactly once.
Anybody can check these by hand or computer if they want to verify them.

[TomZ]

Using a set of algorithms to generate a random state isn't optimal, there is a possibility for more time to be saved. Please take no offense, but I've taken Jaap's optimal pyraminx solver and mixed it in with the current pyraminx scrambler to produce a random state optimal pyraminx scrambler.

In theory it should work, but I have no clue on how to properly scramble a pyraminx, and the color scheme on mine seems to be different from the standard one so verifying the scrambles is hard for me. Could somebody please try it and tell me if the scrambles match the pictures? Link: http://www.zandenonline.nl/pyrascrambler.html

[Lucas]

Using a set of algorithms to generate a random state isn't optimal, there is a possibility for more time to be saved. Please take no offense, but I've taken Jaap's optimal pyraminx solver and mixed it in with the current pyraminx scrambler to produce a random state optimal pyraminx scrambler.

In theory it should work, but I have no clue on how to properly scramble a pyraminx, and the color scheme on mine seems to be different from the standard one so verifying the scrambles is hard for me. Could somebody please try it and tell me if the scrambles match the pictures? Link: http://www.zandenonline.nl/pyrascrambler.html

There's not only a possibility, it's a necessity.
I didn't want to use Jaap's code, though, but I wasn't going to write a full solver myself.

Anyhow, your pictures don't match.

[TomZ]

I think they should match now. Could you please give it another try?

[jbcm627]

I think they should match now. Could you please give it another try?

Still doesn't work for me, although it seems very close... I had to do an [l'] rotation before twisting the tips for it to match, and probably related, some of the colors were mixed up.

And I knew IE had its advantages... why do the images look so funny in FF?

Edit: I modified the draw_triangle function to make them appear ok:

Code: Select all

function draw_triangle(pat, color, val)
{
   var s = "";
   if(pat == 1) {
      s += "<table border=0 cellpadding=0 cellspacing=0>";
      s += "<tr>";
      for(var c=1; c<=12; c++){
         s += "<td width=1 height=2 bgcolor=" + colorList[colors[color] + 2] + ">" + val+  "</td>";
      }
      s += "</tr>";
 
      for(var i = 1; i <= 5; i++) {
         s += "<tr>";
         s += "<td colspan=" + i + " width=" + i + " height=2 bgcolor=silver></td>";
         s += "<td colspan=" + (12 - i * 2) + " width=" + (12 - i * 2) + " height=2 bgcolor=" + colorList[colors[color] + 2] + "></td>";
         s += "<td colspan=" + i + " width=" + i + " height=2 bgcolor=silver></td>";
         s += "</tr>";
      }
 
      s += "</table>";
   }
   else if(pat == 2) {
      s += "<table border=0 cellpadding=0 cellspacing=0>";
      for(var i = 5; i >= 1; i--) {
         s += "<tr>";
         s += "<td colspan=" + i + " width=" + i + " height=2 bgcolor=silver></td>";
         s += "<td colspan=" + (12 - i * 2) + " width=" + (12 - i * 2) + " height=2 bgcolor=" + colorList[colors[color] + 2] + "></td>";
         s += "<td colspan=" + i + " width=" + i + " height=2 bgcolor=silver></td>";
         s += "</tr>";
      }

      s += "<tr>";
      for(var c=1; c<=12; c++){
         s += "<td width=1 height=2 bgcolor=" + colorList[colors[color] + 2] + ">" + val+  "</td>";
      }
      s += "</tr>";
      s += "</table>";
   }
   else {
      s += "&nbsp;";
   }
   return s;
}