The following is the result of a discussion with Thomas Dorf Nielsen <tdn@vrcn.dk> in early December, 2000. We were discussion the 7 white to 2 red colour cycle I used in my own twist tube. Thomas himself was figuring out the colours and construction methods to use in his own twist tube.
Also included is the method I use to figure out the which piece needs which colour, and the numbers of those pieces.
If anyone on the net makes one of these variations, or something completely different, please let us know. Better still send a photo (or a URL to a photo)!
An easy way to think and to check just how many pieces you need is to draw up a slanted grid a bit like the ASCII art below. Remember as a tube the top edge would join the bottom edge. Ignore the side bulge for this purpose. Include the pieces #1 to #8 at each end so you can figure the colour for each piece (which is what I did).
The 7 to 2 ratio was chosen as that adds up to a nine piece colour cycle on the tube which has 8 pieces going around. That is, the colour spirals around the completed tube. 2 reds were chosen so the colours would overlap slightly at the joins, so the spiral did not appear disjointed.
ASCII art time: '.
' white '*
' red..
.../......./......./......./......./... ../......./......./......./......./**** ./......./......./......./*******/***** /......./......./*******/*******/...... ......./*******/*******/......./....... ******/*******/......./......./......./ *****/......./......./......./......./. ..../......./......./......./......./.. |
However 5 of one colour and 4 of another colour will produce that same spiral as the 7 white and 2 red, just a thicker strip with almost equal ratio of red and white. Of course you could adjust the slant to cord length ratio so as to make it an odd number, allowing you to use an exactly equal ratio of colors spiralling around the tube.
Just alternating colours in this design will result in a straight stripes down the length of the tube. That is one colour will match to the same colour in the next spiral loop of the tube (8 pieces further down).
NOTE: with the original 8 piece tube plan, you can make a spiral from equal amounts of 3 colours (9 colour cycle on a 8 piece cycle tube).
Making the #9 pieces from 3 colours has even more possibilities, and even more work. IE: the red stripe is only on the top of the bulge, not at the ends.
Thinking about it, and you will see you need to start two bulges from the front of the tube. EG: for a 8 piece around tube...
***/.../***/.../***/.../***/.../** **/.../***/.../***/.../***/.../*** */.../***/.../***/.../***/.../***/ /.../***/.../***/.../***/.../***/. .../***/.../***/.../***/.../***/.. ../***/.../***/.../***/.../***/... ./***/.../***/.../***/.../***/.../ /***/.../***/.../***/.../***/.../* |
If the colours were red and white you would essentially end up with a rotating 'barber pole', adding a ball on the end would enhace that look.
From the above discussion, Thomas Dorf Nielsen developed the plan for a
Double Twisty Tube