T Hull

WIP – a duo of interlinked Torusses

| wonko

For Xmas, my son Matt gave me a day a page Gary Larson desk calendar. Knowing me, I noticed the tear-off pages were square so, in a moment of madness I decided to fold something with ALL of it:

Exploring scale (and remembering the disaster in finished size that was my last attempt at a torus), I decided a PHIZZ based structure would be fun, with a torus being suitably visually interesting so set about folding units for them from the quartered pages. After 3 months I had enough (360+) to connect up the first torus, then began accumulating units for the planned second.

A longitudinal fold like this requires patience and persistence – making any part of the structure required LOTS of units, so you just gotta wait for the days to go by,

During July, I had enough units to complete the second Torus, deciding they needed to be interlinked, and began to work out HOW to connect up the units while being connected to another torus. Logistically this ramps up the difficulty exponentially – coupled with the fact that I initially connected the loop INSIDE OUT, requiring me to unpick it and invert it before re-joining it.

I am not sure if the inside diameter of the donut hole is wide enough to have 2 torusses passing through it – I _think_ it will be ok with a small amount of squishing, but I guess we will find out in 3 months.

The resultant dual torus chain is visually awesome, the geometry of 5,6 and 7-sided polygon meshes that comprise the curves are really interesting to look at, and it sort of self-supports, making display fun.

Folding over such an elongated period of time is exhausting. Keeping the model save and clean for that time so it all looks like it was made together is also a challenge I am currently working through.

Half way through the journey and i am still keen … we shall see how long that lasts.

Torus

| wonko

When gifted a Larson a Day tear off calendar (thanks Matt), I was faced with a problem – each tear off day is a perfect square and there are 365 of them (for the year), and … I obsessively fold paper so naturally:

This is a 360 unit modular, based on Tom Hull’s Phizz unit – sort of origami lego.

The construction relies on inherent curvature of clusters of units. If you link 6 into a hexagon, the resultant shape is flat. Less than 6 units and the structure curves into a bump (ie. positive curvature), and groups of 7 or more negatively curve (like a saddle).

The basic structure is an inner strip of 6s, either side is a strip of 7s – this then forms the middle of the donut. A strip of 6s, then a strip of 5s to outcurve and then a strip of 6s to close – sounds more complicated than it is, but boy is it fiddly. Docking 3 phizz units together requires interleaving layers over a bend – when there is nothing else in the way it is simple, when there is lots surrounding it then it becomes very difficult, particularly when you cannot reach both sides of the join in the later stages of lacing it up.

The result is lovely, the geometry draws the eye. This used up what will be 1/4 of the total sheets torn off for the year – whether I keep going is up in the air at the moment – long term projects are fun so we shall see.

1128: Origami Computer

| wonko

For a system to be considered “Turing Complete”, it must be able to be used for completing any computational problem. In the world of DIGITAL Turing Complete setups, these computations are achieved using simpler binary operations (like NOT, AND, OR, NOR, etc.).

In a paper recently released by Mathematicians Thomas C. Hull and Inna Zakharevich, they propose flat-foldable crease patterns for origami “processors” that simulate a number of simple binary operations (namely NAND, NOR, AND, OR, NOT and a few ancillary operations) making the theoretical proposition that flat foldable origami is Turing Complete.

I folded a few of the paper’s logic gates, and made a video of how they work – have a look:

Although this is a little nerdy, I can at least conceptualise the idea that a network of interconnected origami processors could, theoretically, actually do something useful. Technical challenges exist with having such crease patterns co-exist on the same sheet, in sufficient quantities to represent anything other than single bits (0/1 or On/Off or True/False), but the idea is none the less tantalising.

I link to a copy of the paper here: FLAT ORIGAMI IS TURING COMPLETE

460: Torus

| wonko

Christmas is just around the corner, so I was thinking “wreath” shapes and stumbled across an astonishing torus made entirely of Tom Hull’s “Phizz” units:

The structure is based on twisted units that combine in 5’s (a pentagon has positive curvature), 6’s (a hexagon has zero curvature) and 7’s (a heptagon has negative curvature).

The inside has 10 heptagons and hexagon spacers, the outer rim has 10 pentagons with hexagon spacers and the rest of the shapes are hexagons.

This shape does my head in – heptagons take up more paper yet less space in the shape … huh? Negative curvature makes the inside of the donut by making a series of “saddles” which is pretty neat. Continue reading →

411: Phizz-based Stellated Icosahedron

| wonko

The “phizz” unit designed by Tom Hull is a basic building block that can be used for many modulars:

I thought I would start manageable, so devised a 30 unit ball, 6 faces each of 5 colours – total of 30 units. These are easy folding and have a positive locking mechanism so were a good choice.

The tricksey part was to ensure an even colour balance – making sure that no face has the same colour twice. that did my head in a little, and it seemd to take me ages to come up with a construction method where I could easily predict what colour next to use.

In the end, a lovely modular – I may try for something grander, we shall see.