visualizing superpositions

Superpositions can sometimes be somewhat abstract. But today I want to show that it is quite easy to visualize them. Though I had to write a little python, and dig up an old gnuplot script.

Here is the new python (not super happy with the name, but it will do for now):
def hash_data(one,size):
  logger.debug("hash-data one: " + str(one))
  logger.debug("hash-data size: " + size)
  try:
    size = int(size)
  except:
    return ket("",0)
  array = [0] * (16**size)
  for x in one:
    our_hash = hashlib.md5(x.label.encode('utf-8')).hexdigest()[-size:]
    k = int(our_hash,16)
    array[k] += 1 * x.value
  logger.info("hash-data writing to tmp-sp.dat")
  f = open('tmp-sp.dat','w')
  for k in array:
    f.write(str(k) + '\n')
  f.close()
  return ket("hash-data")
Now, I have an example in mind that would be good to visualize. Recall:
sa: load improved-imdb.sw
sa: table[actor,coeff] common[actors] select[1,6] self-similar[actors] |movie: Star Trek: The Motion Picture (1979)>
+-------------------+-------+
| actor             | coeff |
+-------------------+-------+
| James Doohan      | 0.109 |
| DeForest Kelley   | 0.109 |
| Walter (I) Koenig | 0.109 |
| Leonard Nimoy     | 0.109 |
| William Shatner   | 0.109 |
| George Takei      | 0.109 |
| Nichelle Nichols  | 0.109 |
+-------------------+-------+
Now, in the console:
sa: load improved-imdb.sw
sa: |result> => self-similar[actors] |movie: Star Trek: The Motion Picture (1979)>

sa: hash-data[4] |movie: Star Trek: The Motion Picture (1979)>
sa: hash-data[4] "" |result>
sa: hash-data[4] select[1,6] "" |result>
sa: hash-data[4] common[actors] select[1,6] "" |result>
Then we make use of this script($ ./make-image.sh tmp-sp.dat), and then we have:
Anyway, I think that is cool. And is approaching what I imagine a brain would look like.

BTW, I should mention. The spikes in the first three graphs correspond to movies, and the spikes in the last graph correspond to the original series Star Trek actors.

Update: one more step to another superposition:
-- find all the movies the 7 original series Star Trek actors starred in:
sa: hash-data[4] movies common[actors] select[1,6] "" |result>
Now, out of interest, how many movies was that?
sa: how-many movies common[actors] select[1,6] "" |result>
|number: 262>
What were the top 30 of these?
sa: table[movie,coeff] 100 select[1,30] coeff-sort movies common[actors] select[1,6] "" |result>
+---------------------------------------+--------+
| movie                                 | coeff  |
+---------------------------------------+--------+
| Road Trek 2011 (2012)                 | 76.562 |
| Star Trek Adventure (1991)            | 76.562 |
| The Search for Spock (1984)           | 76.562 |
| The Voyage Home (1986)                | 76.562 |
| The Final Frontier (1989)             | 76.562 |
| The Undiscovered Country (1991)       | 76.562 |
| The Motion Picture (1979)             | 76.562 |
| The Wrath of Khan (1982)              | 76.562 |
| Trekkies (1997)                       | 76.562 |
| To Be Takei (2014)                    | 54.688 |
| Generations (1994)                    | 32.812 |
| Bug Buster (1998)                     | 21.875 |
| Loaded Weapon 1 (1993)                | 21.875 |
| Backyard Blockbusters (2012)          | 21.875 |
| FedCon XXI (2012)                     | 21.875 |
| The Captains (2011)                   | 21.875 |
| Unbelievable!!!!! (2014)              | 21.875 |
| Coneheads (1993)                      | 21.875 |
| The 6th People's Choice Awards (1980) | 21.875 |
| 36 Hours (1965)                       | 10.938 |
| Actors in War (2005)                  | 10.938 |
| Amore! (1993)                         | 10.938 |
| Bus Riley's Back in Town (1965)       | 10.938 |
| Double Trouble (1992/I)               | 10.938 |
| Jigsaw (1968)                         | 10.938 |
| Man in the Wilderness (1971)          | 10.938 |
| New York Skyride (1994)               | 10.938 |
| One of Our Spies Is Missing (1966)    | 10.938 |
| Pretty Maids All in a Row (1971)      | 10.938 |
| River of Stone (1994)                 | 10.938 |
+---------------------------------------+--------+
And what does this look like?
Filter down to the top 9 of these movies:
sa: table[actor,coeff] select[1,9] 100 select[1,30] coeff-sort movies common[actors] select[1,6] "" |result>
+---------------------------------+--------+
| actor                           | coeff  |
+---------------------------------+--------+
| Road Trek 2011 (2012)           | 76.562 |
| Star Trek Adventure (1991)      | 76.562 |
| The Search for Spock (1984)     | 76.562 |
| The Voyage Home (1986)          | 76.562 |
| The Final Frontier (1989)       | 76.562 |
| The Undiscovered Country (1991) | 76.562 |
| The Motion Picture (1979)       | 76.562 |
| The Wrath of Khan (1982)        | 76.562 |
| Trekkies (1997)                 | 76.562 |
+---------------------------------+--------+
And who were the actors in the top 9 of these movies?
sa: table[actor,coeff] coeff-sort actors select[1,9] 100 select[1,30] coeff-sort movies common[actors] select[1,6] "" |result>
+--------------------------+---------+
| actor                    | coeff   |
+--------------------------+---------+
| James Doohan             | 689.062 |
| DeForest Kelley          | 689.062 |
| Walter (I) Koenig        | 689.062 |
| Leonard Nimoy            | 689.062 |
| William Shatner          | 689.062 |
| George Takei             | 689.062 |
| Nichelle Nichols         | 689.062 |
| Grace Lee Whitney        | 382.812 |
| Mark Lenard              | 306.25  |
| Teresa E. Victor         | 229.688 |
| Majel Barrett            | 229.688 |
| Catherine (I) Hicks      | 153.125 |
| Harve Bennett            | 153.125 |
| Merritt Butrick          | 153.125 |
| Gary Faga                | 153.125 |
| Stephen Liska            | 153.125 |
| Robin (I) Curtis         | 153.125 |
| Michael Berryman         | 153.125 |
| Brock Peters             | 153.125 |
| John Schuck              | 153.125 |
| Michael (I) Snyder       | 153.125 |
| Judy Levitt              | 153.125 |
| Todd (I) Bryant          | 153.125 |
| David (I) Warner         | 153.125 |
| Michael (I) Dorn         | 153.125 |
| Tom Morga                | 153.125 |
| Richard (III) Arnold     | 153.125 |
| James T. Kirk            | 153.125 |
| Christopher (I) Flynn    | 76.562  |
| Malcolm McDowell         | 76.562  |
| Patrick (I) Stewart      | 76.562  |
| Gene Roddenberry         | 76.562  |
| Phillip R. Allen         | 76.562  |
| Steve Blalock            | 76.562  |
| David Cadiente           | 76.562  |
| Charles (I) Correll      | 76.562  |
| Bob K. Cummings          | 76.562  |
| Joe W. Davis             | 76.562  |
| Miguel (I) Ferrer        | 76.562  |
| Conroy Gedeon            | 76.562  |
| Robert Hooks             | 76.562  |
| Al (II) Jones            | 76.562  |
| John Larroquette         | 76.562  |
| Christopher (I) Lloyd    | 76.562  |
| Stephen (I) Manley       | 76.562  |
| Eric Mansker             | 76.562  |
| Mario Marcelino          | 76.562  |
| Scott McGinnis           | 76.562  |
| Allan (I) Miller         | 76.562  |
| Phil (I) Morris          | 76.562  |
| Danny Nero               | 76.562  |
| Dennis (I) Ott           | 76.562  |
| Vadia Potenza            | 76.562  |
| Branscombe Richmond      | 76.562  |
| Doug Shanklin            | 76.562  |
| James Sikking            | 76.562  |
| Paul (II) Sorensen       | 76.562  |
| Carl Steven              | 76.562  |
| Frank Welker             | 76.562  |
| Philip Weyland           | 76.562  |
| Judith (I) Anderson      | 76.562  |
| Jessica Biscardi         | 76.562  |
| Katherine Blum           | 76.562  |
| Judi M. Durand           | 76.562  |
| Claudia Lowndes          | 76.562  |
| Jeanne Mori              | 76.562  |
| Nanci Rogers             | 76.562  |
| Kimberly L. Ryusaki      | 76.562  |
| Cathie Shirriff          | 76.562  |
| Rebecca Soladay          | 76.562  |
| Sharon Thomas Cain       | 76.562  |
| Joseph Adamson           | 76.562  |
| Vijay Amritraj           | 76.562  |
| Mike Brislane            | 76.562  |
| Scott DeVenney           | 76.562  |
| Tony (I) Edwards         | 76.562  |
| David Ellenstein         | 76.562  |
| Robert Ellenstein        | 76.562  |
| Thaddeus Golas           | 76.562  |
| Richard Harder           | 76.562  |
| Alex Henteloff           | 76.562  |
| Greg Karas               | 76.562  |
| Joe Knowland             | 76.562  |
| Joe (I) Lando            | 76.562  |
| Everett (I) Lee          | 76.562  |
| Jeff (I) Lester          | 76.562  |
| Jeffrey (I) Martin       | 76.562  |
| James Menges             | 76.562  |
| John (I) Miranda         | 76.562  |
| Tom Mustin               | 76.562  |
| Joseph Naradzay          | 76.562  |
| Marty Pistone            | 76.562  |
| Nick Ramus               | 76.562  |
| Phil Rubenstein          | 76.562  |
| Bob Sarlatte             | 76.562  |
| Raymond Singer           | 76.562  |
| Newell (II) Tarrant      | 76.562  |
| Kirk R. Thatcher         | 76.562  |
| Mike Timoney             | 76.562  |
| Donald W. Zautcke        | 76.562  |
| Monique DeSart           | 76.562  |
| Madge Sinclair           | 76.562  |
| Eve (I) Smith            | 76.562  |
| Viola Kates Stimpson     | 76.562  |
| Jane Wiedlin             | 76.562  |
| Jane (I) Wyatt           | 76.562  |
| Charles (I) Cooper       | 76.562  |
| Gene Cross               | 76.562  |
| Rex (I) Holman           | 76.562  |
| Laurence Luckinbill      | 76.562  |
| George (I) Murdock       | 76.562  |
| Bill (I) Quinn           | 76.562  |
| Carey Scott              | 76.562  |
| Jonathan (I) Simpson     | 76.562  |
| Mike (I) Smithson        | 76.562  |
| Steve Susskind           | 76.562  |
| Cynthia Blaise           | 76.562  |
| Cynthia Gouw             | 76.562  |
| Beverly Hart             | 76.562  |
| Melanie Shatner          | 76.562  |
| Spice Williams-Crosby    | 76.562  |
| Rene Auberjonois         | 76.562  |
| John (II) Beck           | 76.562  |
| John (III) Bloom         | 76.562  |
| Jim (I) Boeke            | 76.562  |
| Michael Bofshever        | 76.562  |
| Carlos Cestero           | 76.562  |
| Barron Christian         | 76.562  |
| Edward Clements          | 76.562  |
| BJ (I) Davis             | 76.562  |
| Douglas (I) Dunning      | 76.562  |
| Robert (I) Easton        | 76.562  |
| Doug Engalla             | 76.562  |
| Trent Christopher Ganino | 76.562  |
| Darryl Henriques         | 76.562  |
| Matthias Hues            | 76.562  |
| Boris Lee Krutonog       | 76.562  |
| James Mapes              | 76.562  |
| Alan (II) Marcus         | 76.562  |
| David Orange             | 76.562  |
| Christopher (I) Plummer  | 76.562  |
| Brett (I) Porter         | 76.562  |
| Douglas (I) Price        | 76.562  |
| Jeremy (I) Roberts       | 76.562  |
| Paul Rossilli            | 76.562  |
| Leon Russom              | 76.562  |
| Clifford Shegog          | 76.562  |
| William Morgan Sheppard  | 76.562  |
| Christian Slater         | 76.562  |
| Kurtwood Smith           | 76.562  |
| Eric A. Stillwell        | 76.562  |
| Angelo Tiffe             | 76.562  |
| J.D. Walters             | 76.562  |
| Kim Cattrall             | 76.562  |
| Shakti Chen              | 76.562  |
| Rosanna DeSoto           | 76.562  |
| Iman (I)                 | 76.562  |
| Katie (I) Johnston       | 76.562  |
| Jimmie Booth             | 76.562  |
| Ralph Brannen            | 76.562  |
| Roger Aaron Brown        | 76.562  |
| Ralph Byers              | 76.562  |
| Stephen (I) Collins      | 76.562  |
| Vern Dietsche            | 76.562  |
| Christopher Doohan       | 76.562  |
| Montgomery Doohan        | 76.562  |
| Dennis (I) Fischer       | 76.562  |
| Joshua Gallegos          | 76.562  |
| David Gautreaux          | 76.562  |
| David Gerrold            | 76.562  |
| John (I) Gowans          | 76.562  |
| William (I) Guest        | 76.562  |
| Leslie C. Howard         | 76.562  |
| Howard Itzkowitz         | 76.562  |
| Junero Jennings          | 76.562  |
| Jon Rashad Kamal         | 76.562  |
| Joel (I) Kramer          | 76.562  |
| Donald J. Long           | 76.562  |
| Bill (I) McIntosh        | 76.562  |
| Dave Moordigian          | 76.562  |
| Tony (I) Rocco           | 76.562  |
| Michael Rougas           | 76.562  |
| Joel Schultz             | 76.562  |
| Franklyn Seales          | 76.562  |
| Norman (I) Stuart        | 76.562  |
| Craig (VII) Thomas       | 76.562  |
| Billy Van Zandt          | 76.562  |
| Paul (III) Weber         | 76.562  |
| Scott (II) Whitney       | 76.562  |
| Michele Ameen Billy      | 76.562  |
| Celeste Cartier          | 76.562  |
| Lisa Chess               | 76.562  |
| Paula Crist              | 76.562  |
| Cassandra (I) Foster     | 76.562  |
| Edna Glover              | 76.562  |
| Sharon Hesky             | 76.562  |
| Sayra Hummel             | 76.562  |
| Persis Khambatta         | 76.562  |
| Marcy Lafferty           | 76.562  |
| Iva Lane                 | 76.562  |
| Jeri McBride             | 76.562  |
| Barbara Minster          | 76.562  |
| Ve Neill                 | 76.562  |
| Terrence (I) O'Connor    | 76.562  |
| Susan (I) O'Sullivan     | 76.562  |
| Louise Stange-Wahl       | 76.562  |
| Bjo Trimble              | 76.562  |
| Momo Yashima             | 76.562  |
| Steve (I) Bond           | 76.562  |
| Brett Baxter Clark       | 76.562  |
| Tim Culbertson           | 76.562  |
| Ike Eisenmann            | 76.562  |
| John (II) Gibson         | 76.562  |
| Nicholas Guest           | 76.562  |
| James Horner             | 76.562  |
| Paul (I) Kent            | 76.562  |
| Dennis Landry            | 76.562  |
| Cristian Letelier        | 76.562  |
| Joel Marstan             | 76.562  |
| Jeff (II) McBride        | 76.562  |
| Roger Menache            | 76.562  |
| Ricardo Montalban        | 76.562  |
| David Ruprecht           | 76.562  |
| Judson Scott             | 76.562  |
| Kevin Rodney Sullivan    | 76.562  |
| Russell Takaki           | 76.562  |
| Deney Terrio             | 76.562  |
| John (I) Vargas          | 76.562  |
| Paul (I) Winfield        | 76.562  |
| John (I) Winston         | 76.562  |
| Kirstie Alley            | 76.562  |
| Laura (I) Banks          | 76.562  |
| Bibi Besch               | 76.562  |
| Dianne (I) Harper        | 76.562  |
| Marcy Vosburgh           | 76.562  |
| Buzz Aldrin              | 76.562  |
| G.Z. Allen               | 76.562  |
| Robert (XII) Allen       | 76.562  |
| Thomas Anitzberger       | 76.562  |
| Michael Armendariz       | 76.562  |
| Thomas Bax               | 76.562  |
| Robert (I) Beltran       | 76.562  |
| Craig Berthiaume         | 76.562  |
| Jared Bird               | 76.562  |
| Robert Boudrow           | 76.562  |
| Denis (I) Bourguignon    | 76.562  |
| Richard (II) Bowen       | 76.562  |
| Brannon Braga            | 76.562  |
| LeVar Burton             | 76.562  |
| Miguel Carreon           | 76.562  |
| Richard Clabaugh         | 76.562  |
| Bruce (III) Clarke       | 76.562  |
| Thomas Clegg             | 76.562  |
| William Coble            | 76.562  |
| Rick Corley              | 76.562  |
| Justin Reid Cutietta     | 76.562  |
| Frank (I) D'Amico        | 76.562  |
| John de Lancie           | 76.562  |
| Brian Dellis             | 76.562  |
| Daren Dochterman         | 76.562  |
| Rey Duran                | 76.562  |
| Ron Duran                | 76.562  |
| Chris (I) Fleming        | 76.562  |
| Jonathan Frakes          | 76.562  |
| Daryl Frazetti           | 76.562  |
| Dennis Friday II         | 76.562  |
| Ross Gabrick             | 76.562  |
| L.D. Gardner             | 76.562  |
| Travis Gates             | 76.562  |
| Michael (III) Gay        | 76.562  |
| Adam Geiss               | 76.562  |
| David Greenstein         | 76.562  |
| Armando Paul Guillen     | 76.562  |
| Peter Haberkorn          | 76.562  |
| Dennis Hanon             | 76.562  |
| Steve (III) Hardy        | 76.562  |
| Scott (III) Harper       | 76.562  |
| Randall Hawthorne        | 76.562  |
| Steve (I) Head           | 76.562  |
| Edward Herndon           | 76.562  |
| Matthew Herra            | 76.562  |
| John Hurles              | 76.562  |
| Devin Irwin              | 76.562  |
| Edgar Jauregui           | 76.562  |
| Richard Koerner          | 76.562  |
| David (I) Koontz         | 76.562  |
| Stephen (I) Koontz       | 76.562  |
| Rich Kronfeld            | 76.562  |
| Gabriel Kerner           | 76.562  |
| Erik (I) Larson          | 76.562  |
| David (I) Livingston     | 76.562  |
| Gary (I) Lockwood        | 76.562  |
| Robert (IV) Lopez        | 76.562  |
| Stanley Lozowsky         | 76.562  |
| Adam Madden              | 76.562  |
| Logan Madden             | 76.562  |
| Geoffrey Mandel          | 76.562  |
| Douglas Marcks           | 76.562  |
| Jason (II) Mathews       | 76.562  |
| Robert Duncan McNeill    | 76.562  |
| Steve Menaugh            | 76.562  |
| Carl (I) Meyers          | 76.562  |
| Tim (I) Meyers           | 76.562  |
| Jason (I) Munoz          | 76.562  |
| Phil Murre               | 76.562  |
| Salvador Nogueda         | 76.562  |
| Robert (I) O'Reilly      | 76.562  |
| Marc Okrand              | 76.562  |
| Rick (I) Overton         | 76.562  |
| Harminder Pal            | 76.562  |
| John Paladin             | 76.562  |
| Ric Parish               | 76.562  |
| Mark Payton              | 76.562  |
| Brian (I) Phelps         | 76.562  |
| Ethan (I) Phillips       | 76.562  |
| Thomas (I) Phillips      | 76.562  |
| Adam (I) Philpott        | 76.562  |
| Robert Picardo           | 76.562  |
| Daniel (I) Pilkington    | 76.562  |
| James Pollnow            | 76.562  |
| Glen Proechel            | 76.562  |
| Michael Raffeo           | 76.562  |
| Russell (I) Ray          | 76.562  |
| Patrick Rimington        | 76.562  |
| Jon (I) Ross             | 76.562  |
| Paul Rudeen              | 76.562  |
| Tim (I) Russ             | 76.562  |
| Robert (X) Russell       | 76.562  |
| Timothy (IV) Scott       | 76.562  |
| Douglas Shannen          | 76.562  |
| Daniel (I) Shea          | 76.562  |
| David (IV) Silverman     | 76.562  |
| Jason Speltz             | 76.562  |
| Brent Spiner             | 76.562  |
| Tom (I) Stewart          | 76.562  |
| Rocky Stinitis           | 76.562  |
| Mark (II) Thompson       | 76.562  |
| Dennis Thuringer         | 76.562  |
| Barron Toler             | 76.562  |
| Kenneth Traft            | 76.562  |
| Fred Travalena           | 76.562  |
| J. Trusk                 | 76.562  |
| Alois C. Tschamjsl       | 76.562  |
| Karl Van Der Wyk         | 76.562  |
| Matt Weinhold            | 76.562  |
| Jonathan (I) West        | 76.562  |
| Michael (I) Westmore     | 76.562  |
| Wil Wheaton              | 76.562  |
| Travis (I) Williams      | 76.562  |
| Wayne Wills              | 76.562  |
| Barbara (II) Adams       | 76.562  |
| Teresa Bailie            | 76.562  |
| Holly Barbour            | 76.562  |
| Morgan Barbour           | 76.562  |
| Roberta Barnhart         | 76.562  |
| Jennifer Bax             | 76.562  |
| Esther Becerra           | 76.562  |
| Viki Beyer               | 76.562  |
| Martha Bock              | 76.562  |
| Jolynn Brown             | 76.562  |
| Nicole Compton           | 76.562  |
| Denise (I) Crosby        | 76.562  |
| Melisa Dahl              | 76.562  |
| Melissa Dahl             | 76.562  |
| Roxann Dawson            | 76.562  |
| Evelyn De Biase          | 76.562  |
| Maria De Maci            | 76.562  |
| Evelyn Eastteam          | 76.562  |
| Ana Espinoza             | 76.562  |
| Terry (I) Farrell        | 76.562  |
| Lynn Fulstone            | 76.562  |
| Glenn Gadd               | 76.562  |
| Laurel Greenstein        | 76.562  |
| Shantell Hafner          | 76.562  |
| Debbie (I) Hanon         | 76.562  |
| Diana Harper             | 76.562  |
| Lisa (III) Harper        | 76.562  |
| Sharron Hawthorne        | 76.562  |
| Joyce Herndon            | 76.562  |
| Inge Heyer               | 76.562  |
| Penny Keane              | 76.562  |
| L. Grace Klitmoller      | 76.562  |
| Margaret Koontz          | 76.562  |
| Joan Letlow              | 76.562  |
| Jane Lostumbo            | 76.562  |
| Joyce (II) Mason         | 76.562  |
| Chase Masterson          | 76.562  |
| Marcella Mesnard         | 76.562  |
| Diane (III) Morgan       | 76.562  |
| Renee Morrison           | 76.562  |
| Kate Mulgrew             | 76.562  |
| Anne Kathleen Murphy     | 76.562  |
| Stephanie (I) Murphy     | 76.562  |
| Carroll Paige            | 76.562  |
| Cheryl Petersen          | 76.562  |
| Shelly Raffeo            | 76.562  |
| Sondra Reynolds          | 76.562  |
| Jessica Rimington        | 76.562  |
| Mary Rottler             | 76.562  |
| Hope Rudeen              | 76.562  |
| Tonya Saunders           | 76.562  |
| Lori Schwartz            | 76.562  |
| Lori Seol                | 76.562  |
| Susan (I) Shea           | 76.562  |
| Wendy (I) Shea           | 76.562  |
| Evan Shride              | 76.562  |
| Donelda Snyder           | 76.562  |
| Helen (I) Souza          | 76.562  |
| Linda Syck               | 76.562  |
| Deborah Taller           | 76.562  |
| Jeri Taylor              | 76.562  |
| Linda Thuringer          | 76.562  |
| Allison (I) Todd         | 76.562  |
| Deborah (II) Warner      | 76.562  |
| Pat Weisner              | 76.562  |
| Deborah Wheeler          | 76.562  |
| Cheryl (III) Wilson      | 76.562  |
+--------------------------+---------+
And what does this look like?
Now, tidy this up by using drop-below[] this time, instead of select[]:
sa: table[actor,coeff] drop-below[150] coeff-sort actors select[1,9] 100 select[1,30] coeff-sort movies common[actors] select[1,6] "" |result>
+----------------------+---------+
| actor                | coeff   |
+----------------------+---------+
| James Doohan         | 689.062 |
| DeForest Kelley      | 689.062 |
| Walter (I) Koenig    | 689.062 |
| Leonard Nimoy        | 689.062 |
| William Shatner      | 689.062 |
| George Takei         | 689.062 |
| Nichelle Nichols     | 689.062 |
| Grace Lee Whitney    | 382.812 |
| Mark Lenard          | 306.25  |
| Teresa E. Victor     | 229.688 |
| Majel Barrett        | 229.688 |
| Catherine (I) Hicks  | 153.125 |
| Harve Bennett        | 153.125 |
| Merritt Butrick      | 153.125 |
| Gary Faga            | 153.125 |
| Stephen Liska        | 153.125 |
| Robin (I) Curtis     | 153.125 |
| Michael Berryman     | 153.125 |
| Brock Peters         | 153.125 |
| John Schuck          | 153.125 |
| Michael (I) Snyder   | 153.125 |
| Judy Levitt          | 153.125 |
| Todd (I) Bryant      | 153.125 |
| David (I) Warner     | 153.125 |
| Michael (I) Dorn     | 153.125 |
| Tom Morga            | 153.125 |
| Richard (III) Arnold | 153.125 |
| James T. Kirk        | 153.125 |
+----------------------+---------+
And our final graph:
Anyway, lots of fun. I hope it is now easier to visualize what happens as we step from superposition to superposition.

OK. I think it might be interesting to show them all at once, in sequence:



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updated: 19/12/2016
by Garry Morrison
email: garry -at- semantic-db.org