Tessellated I - my simple technical drawing, coloured artfully

Replies

• 

  Ramani Aswath

  Peter Dow

  

  Beautiful work, Peter. Very satisfying and dynamic. Thanks for putting up.
  Reminds me of the Shepard-Risset Glissando
  
  #-Link-Snipped-#
• 

  Peter Dow

  bioramani

  Beautiful work, Peter. Very satisfying and dynamic. Thanks for putting up.

  Thanks Bioramani but I'm responsible only for the precise detail of my "Tessellated I" than the beauty which I think comes mostly from piece's colour scheme which was Cori Davis's original creation and so the thanks for the beauty are due to her, not me.
  
  My interpretation of her art work is a digitized, neat and flawless technical CAD drawing compared to Cori Davis's more spontaneous, natural and charming free-hand art work.
  
  One might say that a doll looks beautiful but that's mostly because a doll is a man-made likeness of a real child which has a far superior natural beauty.
  
  But my image did require some effort to produce so I will accept some thanks for what I did .
  
  

  bioramani

  Reminds me of the Shepard-Risset Glissando
  
  #-Link-Snipped-#

  Well I had considered the obvious shape and colour aspects of my image but had not even considered that the work had a sound parallel, or perhaps you are comparing this work to the visualisations which appear on the videos you link to?
  
  The sound comparison I would make is with the performance of a piece of classical music. The performers play Beethoven and get applause from the audience at the end for the performance and the interpretation of the music, even though everyone knows that the true artistic genius was the composer, Beethoven, not the musicians.
  
  The comparison is that I have only interpreted the work of Cori Davis and she is true artistic genius, not me.
  
  I note that the Imageshack server is refusing to serve the image I posted so here it is again served from another server.
  
  
  
  
  Some find the colours too bright and saturated, too vivid for their taste so I have produced a 66% colour saturated version.
  
  
  
  Also, I can rotate the image by 90 degress to give a "Tessellated H", so to speak.
  
  
  
  That's the orientation that Cori Davis's art work is in though her shape is more an "I"-on-its-side than an "H".
• 

  Ramani Aswath

  What I felt was that depending on the way one looks at it (the 'I' version) one can see endless steps going down from right to left. Also reds and yellows tend to pop out of the paper because of the way we perceive colours. What is a static design suddenly comes alive because of the interesting interplay of colours.
  
  Ye hae a guid yak, man!
• 

  Peter Dow

  Now this is all my own creation, also produced using Paint.NET.
  
  Tessellated I in Steel
  
  
  
  #-Link-Snipped-#
  
  Now it's time to think about possible engineering applications.
• 

  Ramani Aswath

  This structure will have some flexibility in two dimensions. The interlocking 'I's will give excellent tensile strength. Some sort of strong flex covering roofs, flooring and even walls perhaps. Solar panels?
• 

  Peter Dow

  bioramani

  This structure will have some flexibility in two dimensions. The interlocking 'I's will give excellent tensile strength.

  Of course a real structure always has 3 dimensions to it but considering the 2 dimensional tessellated-I pattern I have posted here first of all then be careful because this tessellation-I 2D pattern only automatically interlocks a structure of tiles in 1 of the 2 dimensions, whereas in the other dimension there is no automatic interlock which arises purely from the 2D shape.
  
  We can consider the 2D properties by imagining that simple flat I-tessellated tiles are siting on a smooth flat horizontal surface - the floor or a table-top.
  
  Then the tensile properties of the 2D structure of tiles as a whole are extremely dependent on the direction along which a tensile force is applied.
  
  If a tensile force is applied to the tiles structure along the direction of the rows of Is
  
  << IIIIIIIIIIIIIIII >>
  
  there is no tensile strength whatsoever! The structure is loose and comes apart, unless the tiles are stuck to the floor or table-top with cement or glue!
  
  If a tensile force is applied to the structure along a column of Is
  
  ^
  ^
  
  I
  I
  I
  I
  I
  I
  I
  
  V
  V
  
  
  the tensile strength at best is one quarter of the tensile strength of the material from which the tile is constructed.
  
  Therefore to construct a cohesive tessellated-I structure in 3 dimensions one must solve the problem of the lack of any tensile strength in one of the dimensions of the 2D shape either by sticking or bolting or otherwise joining the tiles to each other or onto a solid surface with its own useful tensile properties.
  
  I presume you are assuming a fairly simple 3D I-tile shape which is the simplest extension of my 2D I into three dimensions, namely with the same cross sectional I-shape in the 3rd dimension of the tile, something like we might expect to see in paving stones
  
  
  
  or wall tiles?
  
  
  
  For such simple tile shapes, the properties of the surface the paving stones are laying on or walls tile are mounted on, and the strength of the bond between tiles and surface contributes significantly to determine the overall properties of the structure, yes?
  
  I don't think it is too wise to boast of the tensile properties of any structure composed of tessellated-I tiles until one has specified how they will all be held together.
  
  Also once everything is stuck down or on one may well find that the flexibility is not quite what once one had hoped depending on exactly how it is all stuck together.
  
  

  bioramani

  Some sort of strong flex covering roofs, flooring and even walls perhaps. Solar panels?

  Yes, I think those could all be done in this pattern although whether in each case it would be worth doing this way would depend on what advantages if any were to found by making the structure in this fashion.
  
  The disadvantage is that it is new and complicated to introduce these I-shaped tiles where before the job was usually done with simpler square or rectangular etc shaped tiles.
  
  Well I find this question interesting anyway. Perhaps my next step is to consider how to make 3-D models of tessellated-I structures, experimenting with various concepts of how it might be held together. Here various kids building toys such as Meccano and Lego could be my inspiration.
  
  
• 

  Ramani Aswath

  I was considering the pattern of the interlocked tiles that you mentioned;
  

  I presume you are assuming a fairly simple 3D I-tile shape which is the simplest extension of my 2D I into three dimensions, namely with the same cross sectional I-shape in the 3rd dimension of the tile, something like we might expect to see in paving stones

  Some sort of curtain like covering on inclined or even vertical surfaces. Of course it may not work as a structural member. However it can accommodate rather irregular surfaces.
• 

  Peter Dow

  bioramani

  I was considering the pattern of the interlocked tiles that you mentioned;

  So was I.
  
  I was just pointing out that the interlocking of simple tessellated I-tiles of equal cross-section shape throughout their depth is only in one direction and that whilst the columns of Is are indeed initially interlocked together as columns, the rows of Is are not in any way interlocked together and columns of Is can be separated from their neighbouring columns of Is most easily.
  
  For example if we start with precisely the pattern of tessellated-I tiles I have already mentioned and posted images of but for convenience represent what we are talking about approximately by an arrangement of character Is as follows
  
  

  IIII
  IIII
  IIII

  
  
  then if the tiles are not glued or bolted to each other or to another surface then the columns of tessellated Is could be easily pulled apart from each other first as follows
  
  

  I  I  I  I
  I  I  I  I
  I  I  I  I

  
  
  because columns of tessellated-Is are not interlocked with each other in that direction.
  
  Then after the columns are separated into individual columns there is no longer any interlocking at all and the rows of I tiles can be pulled apart as follows, disassembling the Is from their columns as well
  
  

  I  I  I  I
   
   
  I  I  I  I
   
   
  I  I  I  I

  
  
  leaving all the tiles entirely disconnected from the original arrangement.
  
  This would be easy to demonstrate if I had some I-tiles to make a video of me pulling them apart but initially at least I am wondering if you can look more closely at the interlocking and see that it is not as interlocked in 2-dimensions as you seem to think?
  
  

  bioramani

  Some sort of curtain like covering on inclined or even vertical surfaces. Of course it may not work as a structural member. However it can accommodate rather irregular surfaces.

  All sorts of structures are possible based on tessellated I-tiles but there requires to be specified some method of attaching the columns of I-tiles to each other.
• 

  Peter Dow

  Someone on another forum produced an image - which I have uploaded here - "tiles cracked.jpg" which shows how the simple 2-D shape can be pulled apart without further interlocking features in 3-dimensions, which I will now describe.
  
  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 Tessellated I / H tiles / bricks | Page 1 | Naked Science Forum 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 Tessellated I / H tiles / bricks | Page 1 | Naked Science Forum 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.
• 

  Ramani Aswath

  Since they dovetail or interlock to form structures an obvious name can be Dowtail.
  Saw the video. Good.
• 

  Peter Dow

  bioramani

  Since they dovetail or interlock to form structures an obvious name can be Dowtail.

  Well the pins and tails of a "dovetail" joint are trapezoidal in shape, as is the tail of a dove, but the pins and tails of the joints in my model are not trapezoidal, they are straight, so the word "dove" does not apply to anything in my model or in my 3D design though one could certainly describe the tops and bases of the Is as "pins and tails" of joints and my 3D design does have dowels through those "pins and tails" so yes "doweled-tail" joints would appropriate but surely doweled pins and tails joints have been used many times before now?
  
  Granted that such doweled-tail joints may not be as common or generally useful as dovetail joints but the doweled-tail joints in my model cannot be a first in wood work or metal work, surely?
  
  Woodworkers and metalworkers may think me very strange, crazy even, if I was to agree to put my name to a joining method which they may have used many times before now or perhaps even appears in a book somewhere as a standard method. Then they'd ask "Who does this crazy engineer Dow think he is putting his name to our standard method"?
  
  So I thought that my doweled-tail joints only in the context of my very specific I or H tile and brick tessellated structure needed a specific name and that's why I suggested "Mazurka dowels" in this case and I included the word "dowels" because the tails are straight and unremarkable at first glance whereas the dowels are what makes the joint distinctive from other pins and tails joints.
  
  I mean these paving stones have very similar looking tails, right?
  
  
  
  The tails on my Is are not so different looking from the tails of these paving stones that they'd need a new name like "Dowtail". OK we can presume that those paving stone I tails don't have dowel holes and dowels running through them but the exterior visible shape of the tails is very similar. The things that are most different are the dowels and dowel holes so it is those that need a new name I think, not so much the tails per se.
  
  It was specifically the dowels that Mazurka suggested and what I had got planned but had not posted about so that's why I think the name "Mazurka dowels" is, or maybe "Mazurka doweled joint" might be appropriate, but not "Mazurka tails" or even "Dow tails" because the pins and tails of the joints between bricks and tiles are not, superficially anyway, so unique as to be worthy of a new name.
  
  I assume that such doweled pins and tails joints are generally called something like "doweled joints" or have another general name already, with no need for me to think up a new general name for them, only a new name in the context of my very specific variant of the I or H tile or brick tessellated structure.
  
  Whatever these joints in my design are to be called, we have to mention the dowels, would you not agree? Also "Dow dowels" or "Dow doweled tail joint" or something has too much alliteration to be taken seriously as a name.
  
  

  bioramani

  Saw the video. Good.

  There's nothing quite like a model and a video showing the model from all angles to explain a 3D shape. Yes, you can do something like it with CAD 3D graphical image rendering but in this case the model was not too hard to make so I thought it was best method to choose. I included the still images from the video as well because not everyone has a broadband internet connection that can stream videos from YouTube.
• 

  Peter Dow

  
  
  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.
• 

  Rupam Das

  Wow! Simply great thinking of engineering. The Video is awesome and the pieces are rocking.