Tessellated I - my simple technical drawing, coloured artfully

Peter Dow

Registered Senior Member

View a larger scale version of Tessellated I

A tessellation of a capital "I" shape employing the colours of the spectrum which I created using Paint.NET the free image and photo editing software which runs on Windows.

The "I" Shape.
The "I" shape is square in proportions, with the vertical column one third the width of the square by design. The thickness of the base and top of the "I" are the same thickness and consequently have to be one quarter of the height of the square to tessellate in this precise fashion. The shape of the "I" I arrived at during consideration of one of my engineering design projects.

The Colours.
My use of the colours of the spectrum, half of the "I"s Red-Orange-Yellow and the other half Green-Blue-Purple, and the black lines to define the outline of the "I"s was directly inspired from a work of art I found on DeviantArt website, named "Colorful Tessellation" by ~TheShadowRider123, Cori Davis of the United States of America. This work of art is dedicated to Cori with my thanks for the inspiration her work gave me.

Using Paint.NET I was able to add what I would describe as a "metallic texture" to the colours, although the program function I used is called "Effects - Distort - Dent" by Paint.NET's menus.

This version of the work has my own watermark added.
Tessellated I / H / 66% colour / Steel

The image server has stopped serving that particular image from some unknown reason so here it is again from another server.


I like it.
Thanks C.C.

I sense possible M.C. Escher inspiration.
Well I do have my image featured now in the M-C-Escher-style group on DeviantArt.

But my inspiration is truly a) the engineering possibilities of tessellation shapes - that's inspiration for the "I" shape and b) the artistic colour scheme in Cori Davis's "Colorful Tessellation" - that's inspiration for the colours I used.

It really is a co-incidence that my "Tessellated I" seems related to the work of a very imaginative artist like M.C. Escher but I am very happy to have my technical drawing thought of in that light.

As more of an engineer than an artist, I am more of a fan of tessellations in engineering and nature - pavement slabs, brick walls, honeycombs etc - than I am a fan of the work of a pure artist like M.C. Escher.


Rotate my image by 90 degrees to get "Tessellated H".


Reducing the colour saturation to 66% gives -


Tessellated I in Steel


View larger version of Tessellated I in Steel 1800 x 800

Representing a surface of "I"-shaped steel tiles or an embossed "I" tessellation pattern in a steel sheet. Produced using Paint.NET.

The "I" shape is of square proportions, the column of the I being one third of the width of the square and the top and the base one quarter of the height of the square.
Plane and space tilings are a vast school of study in contemporary geometry.

My personal favourites are the quasiperiodics, though brute - forced pentagonal tilings are also loads of fun, especially in free - forms. There are some very entertaining 3 - space instantiations of quasiperiodic lattices in exotic metal alloys as well.

It may be enjoyable for you to have a quick run - through of the big book on M.C. Escher. (Warning: some of the algebraic relations are inaccurate.) ;) Dover publications has a ton of tessellation collections if you wish to pursue the study of those.
Thank you Stoniphi for your contribution to this topic.

Now I'd like to revisit the purpose of my technical drawing and I mean specifically the non-artistic purposes. Accordingly, I have requested to the moderators that this topic now be moved into the Architecture & Engineering forum.

From the engineering consideration that typical simple tiles and bricks are far from optimal in terms of adding structural strength to constructions such as buildings, walls etc., I am proposing better-designed more robust, more secure tiles / bricks and I believe that further design developments to the I / H - tile / brick 2-dimensional shape I have suggested here - specifically fleshing out the simple 2-D design into a more detailed 3-D design which introduces further efficient tile-to-tile / brick-to-brick interlocking or making-rigid features is a promising way to go.

I still need to develop the 3-D design a bit more because I'd want the tiles or bricks to be able to be assembled together then disassembled when necessary without having to be cemented together like a brick wall


and without having to be glued onto a mounting surface like conventional tiles


So I am looking for a design that allows assembly and disassembly such as with Lego, Meccano or many manufactured products which use such typical features as nuts and bolts and bolt-holes but many other variations to secure one part to another strongly but in a reversible and flexible way. The ability to disassemble is particularly useful for temporary structures, as is strength to weight ratio so that the parts of the structure can be moved easily to where they need to be erected.


So I still have some design thinking and technical drawing to do and then I'll need a fabrication plan. Most likely I'll want to make the tiles or bricks out of metal for strength reasons - although for some applications plastics and in particular fiber-reinforced plastics offer very high strength-to-weight ratios and so may be even better. I'll need to start small with models first and then see if anyone else might be interested in applying the design for real engineering applications?
Now I'd like to revisit the purpose of my technical drawing and I mean specifically the non-artistic purposes. Accordingly, I have requested to the moderators that this topic now be moved into the Architecture & Engineering forum.
I'm reluctant to do that since so far it's been art- and craft-oriented.

Also because I don't get a lot of threads in A&C that are much beyond "Look at this neat thing I just found on the internet, don't you all just love it." I'd hate to lose one. ;)

If anything, I might be persuaded to move it to Math & Physics, since I first learned about tesselation in a math class. Semi-regular tesselations make some interesting art.

Why don't you just start a new thread in A&E? Rewrite your last post for an audience of engineers instead of artists. You can use the same pictures. Meanwhile people who stumble into this thread in A&C will have something fun to discuss.

As your editor I would suggest that you define "tesselation." Sure, it should be obvious but I guarantee some people are going to scratch their heads and say, "I don't get it."
I agree with you, Frag.

I did my Mathematics Masters project on Plane and Space Tilings and opin professionally that it is indeed art.

My son and I loved the heck out of those Duplo blocks when he was small though...they were a real gas to play with. :)
3-Dimensional model video




Tessellated I or H bricks and tiles for stronger, lighter assembled structures (YouTube)

This video shows my model of the 3-dimensional shape of a simple structure composed of 6 bricks or tiles, each of which, when viewed from one-direction anyway, are a 2-dimensional "I"-shape (equally when rotated by 90 degrees "H"-shaped).

This model has been made from aluminium tubing and in order to distinguish one brick from another they have been coloured using marker pens - so there are two bricks coloured blue, two coloured green and two coloured red. This colouring was necessary for clarity because otherwise the permanent joints within bricks (which are only an artifact of the method to make a brick from square tubing) might be confused with the simple touching surface where two neighbouring bricks abut, abutting securely but without being in any way stuck by glue etc.

This 3-Dimensional model reveals a further design feature of the I or H brick and tile structures, which secures the bricks and tiles together in 2 further dimensions, some such feature being necessary because the 2-D I or H shape in of itself only secures the bricks together in 1 dimension.

This feature is revealed here to be nothing more complicated than dowels or fixing rods which run in the vertical direction of the Is (or the horizontal direction of the Hs) through shafts in the Is' bases and tops and which serve to lock the tops and bases of neighbouring Is together, preventing movement radially from the dowels.

These dowels may henceforth be referred to as "Mazurka Dowels" named after the username of a scientist in an internet science forum who first correctly anticipated this feature of my 3-D design and its function to hold the structure together in all 3-dimensions, in a reply post to my topic there describing in detail only the 2-D tessellation, suggesting somewhat vaguely that some such design element was required for a good 3-D design with a view to seeing who would suggest the solution I had thought of first.

As I explained in that topic I could hardly call those dowels the "Dow dowels" there being too many dows in that name and anyway, my name can be used to reference this particular shape of I or H tile and brick and structures composed of them, as per "Dow tile" "Dow brick" "Dow I-tile" "Dow H-brick" "Dow I-H-brick" "Dow I-H-brick structure" "Dow I-structure" etc.
HI-BRICKS & DOWELS demonstration video


HI-BRICKS & DOWELS demonstration video by Peter Dow (YouTube)

Transcript of the video


Hi everybody and welcome to my "H" / "I" Bricks or HI-BRICKS & DOWELS demonstration video.

This is Peter Dow from Aberdeen, Scotland.

There are two components to a HI-BRICKS & DOWELS construction -
  • the BRICKS, which you can either describe as "H"-shaped or "I"-shaped, depending on which way you turn them around
  • and the DOWELS

The shape of the "H" or "I" bricks is designed so that they fit together to form a layer or a wall of bricks and importantly, the bricks, just by their very shape, immobilise each other from moving, in one dimension only.

Let's have a look at that.

Let's consider this green brick here as the fixed point.

We can see that it immobilises its neighbouring bricks in one dimension. They can't move with respect to the green brick in this dimension. So that's locked. Even though there is no bricks here or here, the very shape stops it moving in that dimension.

Now the shape doesn't stop the bricks moving with respect to each other in that direction, or in that direction but they are fixed in that one dimension.


Now if we want to make a rigid structure of bricks in all three dimensions but without using mortar or glue so that we can assemble and disassemble the structure whenever we like, what we need next are the DOWELS.

As you can see, the "I" or "H" bricks have shafts running through the corners so that you can run a dowel through the corners - two shafts, four holes per "I" or "H" brick.

And when you assemble the bricks you can slide the dowel in ... and this forms a structure which is rigid in all three dimensions, which is what we need to form structures.
I really don't want this to come across as just purely critism, because that is not how it's meant. But I do not think you are doing yourself justice in the way in which you are presenting your ideas, for which they do actually appear quite interesting and with some merit. Take example the pictures you have offered of your coloured metal blocks, unfortunately these do look rather amaturish and as if you've just cobbled them together and coloured them in with a felt tip. You really could help generate more interest if you just improve your presentation with a bit more effort and polish. Because afterall do you really want your latest engineering theory dismissed because people think it looks like something that has been knocked up in primary school?. So please let's have the same quality of presentation as that of your actual ideas.
What "weight"? Distributed over what?

A diamond shaped what, for what, in what competition?

You don't half ask some vague questions there river bud.

Peter the reason I mentioned the diamond shape , is based on a building I saw , I think it was discovery channel , not sure though , awhile back , built in Mexico City , which is a very earth quake prone part of the world

I can not remember the name of the building , sorry