Conway's Game of Life
Conway’s Game of Life needs no introduction to fans of Martin Gardner. Numerous examples exist in which a GoL “spaceship” object sends out smaller objects (“gliders”, etc.) that move away from the generator at a constant speed. That speed is set by the underlying nature of the GoL’s generations, because each such object can move no faster -- generation to generation -- than the unit distance built into the GoL model itself. In fact, the maximum such speed of propagation is called c or “the speed of light” in GoL terminology. In a typical computer running a GoL in a lab, the unit of time in the GoL of course has no fixed relationship to the unit of time marked on the lab’s clock on the wall. If the lab personnel were to double the rate of GoL generations (relative to the clock on the wall), the speed at which a GoL glider moves across the screen is also doubled (relative to that clock), but within the GoL universe itself, there is no change in speed.
G4G14
Nathaniel Johnston
Dave Greene
G14-027
Warped-Grid Jig-Saw Puzzle
Puzzle
With a laser-cutter, it is easy to make one-of-a-kind jigsaw puzzles. The question then is what pattern of cuts to use. Here is a gallery of some experiments I have been making in which the cut pattern is based on a warped grid. A pseudorandom grid-based dissection of an underlying rectangular array is distorted to give engaging visual effects.
G4G14
George Hart
G14-028
Octaroller
Puzzle
Recreational Math
BUILD your OCTAROLLER ! from 3 parts square.
RACE your OCTAROLLER ! down the ramp in a straight line.
CHEER your OCTAROLLER ! with supplied cheering pom pom on a toothpick.
Octaroller is included in Geometric Foundations of Design: Old and New -
(Knots and Everything) by Jay Kappraff.
G4G14
Dick Esterle
G14-029
Great Questions for Great Conversations
Game
COVID sometimes gives in unexpected ways. Had G4G14 had taken place March 25 - 29, 2020, my exchange gift would have been a packet of four cards with StoryCorps® Great Questions for Great Conversations and a fifth card with a puzzle.
On account of COVID, many shipments were delayed including colorful envelopes and cards from IndianWeddingCard.com, which I had planned to send out with my 2022 New Year’s letter. Rather than saving them for sending my 2023 New Year’s letter, I have enclosed my G4G14 gift in one of the distinctive envelopes.
G4G14
Nancy Blachman
G14-030
G4G14 Exchange Gift (Martin Gardner Magic Trick)
Magic
Recreational Math
Legacy
We, on behalf of ThinkFun, would like to submit a physical gift based on a personal letter sent from Martin Gardner to one of our founders, Bill Ritchie, in 1994. We will submit photocopies of the letter, which describes how to perform the magic trick. We will also include the pieces needed to perform the magic trick.
G4G14
Bill Ritchie
G14-032
Flippe Top
Toy
This document describes how I designed a new kind of top, which flips not just once, but over and over. I call it a "flippe top". It can be made either from wood or by 3D printing.
G4G14
George Bell
G14-035
Golomb Rulers
Recreational Math
A perfect ruler for daily use. In mathematics, a Golomb ruler is a set of marks at integer positions along a ruler such that no two pairs of marks are the same distance apart.
G4G14
Qingqing Mao
John Bohannon
Yuan Mei
G14-036
Travel Straws
Toy
Re-usable straws in a little keychain-round container with G4G logo (from 2021 conference that was postponed) on it.
G4G14
Delicia Kamins
G14-038
The 14 Two-Color Frieze Symmetries in Mosaic Knitting
Art
Recreational Math
Mosaic knitting, a relatively new form of two-color knitting, has become popular because it is easier for the knitter than most traditional forms of color work. The price of this ease is an unusual set of restrictions on color placement for the pattern designer. Carolyn Yackel and I have researched the impact of these constraints on the symmetries of knitting patterns, culminating in a classification of the color-swapping symmetry groups possible in mosaic knitting.
G4G14
Susan Goldstine
Carolyn Yackel
G14-040
Guess-o-matic
Puzzle
This DIY paper-engineered magic trick performs an astonishing feat of mentalism thanks to a bit of secret mathematics.
G4G14
Adam Rubin
G14-041
StarHex-14: Theo Geerinck's 14 Polystars
Puzzle
Recreational Math
14 tiles consisting of hexagons with 0 to 6 equilateral triangles attached on their edges can be cut from card stock provided to solve the large collection of puzzle figures presented. Five colors, each tile shape is unique with one mirror pair. Rules for two strategy games for two players are included.
This is the printed version of StarHex-I that I make in lasercut acrylic sold on the Kadon website, <a href="http://www.gamepuzzles.com/tiling2.htm#SH14" target="_blank" rel="noreferrer noopener">www.gamepuzzles.com/tiling2.htm#SH14</a>
G4G14
Kate Jones
G14-042
I AM THE RHOMBUS
Puzzle
Recreational Math
In one package: the strip of triangles and brochure for this new flexagon. The colorfully illustrated brochure will include folding directions, flexing directions, and images of the different possible faces.
G4G14
Ann Schwartz
G14-043
14 Blocks
Puzzle
All you have to do is move the large 2x2 block to the bottom right hand corner by sliding the blocks. Do not lift, turn or twist any block.
G4G14
Marti Reis
G14-044
The Accountant
Recreational Math
Legacy
Martin Gardner would sometimes wrap puzzles inside stories he concocted, such as with the book “The Numerology of Dr. Matrix.” The following puts my favorite puzzle in that tradition: The Accountant
by Barney Sperlin
G4G14
Barney Sperlin
G14-046
Walk a Crooked Path
Puzzle
Game
In this puzzle you must find the most crooked path on a board made of squares. Each square is visited at most once, but you need not visit all squares. Your path goes from square to adjacent square, and should have as many 90-degree turns as possible.
G4G14
Jaap Scherphuis
G14-047
Abstract Photograph - Acura TL
Art
Recreational Math
One of my interests is abstract photography, using ordinary photographs as the “paint” and using spatial and mathematical transformations to create an image from one or more sources. One transformation that I’ve been exploring is “Inside Out”, which involves moving the center of the image to the outside and moving the edges of the image to the center. For some source images, the result is a pleasing abstract that doesn’t immediately resemble the source but which contains recognizable elements of the original when you look closely.
G4G14
David L. Kahn
G14-048
A "Pick a Card" Card
Magic
Recreational Math
A card (roughly the size of an index card) with an image that contains 54 playing cards (some duplicates, of course!). A spectator chooses one of the playing cards and, after a few questions, the magician reveals the choice!
The premise is similar to the well-known “pick a number” cards where binary representations are used to identify a mystery number that a spectator has chosen. In this case, the spectator will select any card that he/she sees, and indicate the colors of the squares in which this card is found. The magician then reveals the thought-of card!
Instructions will be printed on the back of the card.
G4G14
John Harris
G14-050
Traveling Through the Sierpinski Carpet and Menger Sponge
Puzzle
Recreational Math
An ant wants to travel from one corner of the Sierpinski carpet to the opposite corner using the shortest possible route. And his friend, a termite, wants to do the same in the Menger sponge. Can you guide them well?
G4G14
Derek Smith
G14-052
Rep-Tile Tangram
Puzzle
Recreational Math
The gift will be a number of cut-out pages to create a rep-tile tangram: A tangram shape that is made from tangram shapes, that are made from tangram shapes.
G4G14
Sabine Segre
G14-053
The Art of Destroying Flexagons
Puzzle
Toy
Recreational Math
Destroying flexagons can be fun and artistic! We suggest 4 different ways to artistically destroy flexagons, each with its own merit. Our exchange gift is a set of 4 flexagons strips, one for each demonstration and the attached explanation sheet.
G4G14
Yossi Elran
G14-054
14 Rabbiducks
Puzzle
Recreational Math
The puzzle is to fit 14 “rabbiduck” polyomino pieces into an 8x11 rectangle. (Gardner wrote about polyominoes in multiple columns. The specific polyomino pieces used are inspired by the rabbit/duck illusion that Gardner called the Rabbitduck in his autobiography.)
14 “Rabbiduck” Pieces that look (crudely) like a rabbit or a duck depending on orientation.
G4G14
Haym Hirsh
G14-055
C.L. Dodgson (Lewis Carroll) Oxford Mathematician
Recreational Math
Word Play
Lewis Carroll, the nom de plume of the Rev. Charles L. Dodgson, a mathematics lecturer at Oxford, was also an innovator in recreational mathematics, magic, puzzles, cryptography, and inventions. His appearances in Scientific American began with mathematician Warren Weaver’s article in April 1956, and his name is mentioned over a hundred times in fourteen of Martin Gardner’s “Mathematical Games” columns. Using these as a springboard, topics will also include Carroll himself, the Wonderland/Looking-Glass dyad, Gardner, and their intertwining in The Annotated Alice.
G4G14
Mark Burstein
Stan Isaacs
Stuart Moskowitz
G14-056
Leaping Crossword No. 2
Puzzle
Game
Word Play
A one-page puzzle with attached solution will be provided, including the instructions for this variant and the clues and grid.
G4G14
Joe DeVincentis
G14-057
Winning Ways HexaFlexagon
Puzzle
Art
Toy
Sadly, all within 13 months of each other, the three authors of the iconic book Winning Ways for Your Mathematical Plays passed away.
Elwyn Berlekamp: Sept 6 1940 – Apr 9 2019
Richard Guy – Sept 30 1916 – Mar 9 2020
John Horton Conway: Dec 26 1937 – Apr 11 2020
All three were friends with Martin and were regulars at the Gathering. Their legacies are grand, and their presence will all be missed.
G4G14
Sean Graves
G14-058
4!-Fold Puzzle
Puzzle
Are there any polycubes that can be unfolded into exactly a rectangle? This problem was solved in 2019. The smallest solution forms a nice puzzle — fold the rectangle into a polycube!
G4G14
Bob Hearn
G14-061