Transcripts
1. The Simple UP/DOWN LEFT/RIGHT Symmetry Group: The only tessellation
I ever copied from MC Escher till this
year was his reptiles, which we covered in the last
class, symmetry group P3. The technique I like to call
the three cozy buddies. Because of these classes, I've had to find examples to
show you other than mine. Therefore, I started taking Escher's tessellations apart
in order to understand them. It has revealed
to me quite a bit about the construction
of a tessellation. I've also included
a few examples of other tessellation artists
with their permission, of course, these other artists will show you the breadth
of styles out there. I've included links to their websites or
social media presences. And of course, they retain the copyrights to
all their artwork, including MC Escher and myself. I will also include the
handout with this information. The arrival of computers. And now tablet has
allowed artists to explore this tessellation are form in greater detail and much faster. The repetitive tasks are gone. Software does the tedious job
of drawing each unit cell. I did start off doing
everything by hand decades ago. And I must say that
it is the best way to learn and understand
the concepts. Yes, I did use scissors and cardboard. There's a big difference though, between looking
at a tessellation and understanding tessellations. Today's technology has
given me a new burst of energy and the desire to
explore this art form again. The results are far ahead of where I used to be with a pencil
and paper. And the software keeps
on getting better. Eric Broug, artist, author and master of Islamic geometric
design recently wrote, and I'm paraphrasing here, that it was all fine
for students to copy the Masters in order
to learn the art form. But a real need was out there for artists to go beyond, beyond copying and modifying
what has come before. I expand the need to
keep the master as our base and explore what is inside ourselves
waiting to burst out, our own inspirations, our
own designs and drawings, and go one step
beyond ourselves. Let's check out the original, the first symmetry group. The symmetry group I like
to call a simple up, down, left, right repetition
of your nested shape.
2. How to Accomplish a Tessellation in this UP/DOWN, LEFT/RIGHT Symmetry Method: MC Escher accomplished
31 tessellations using this symmetry group. It is the most popular
symmetry group to tackle for first timers. The trick consists in
repeating whatever line you have connecting top
and bottom corners of the left edge of
a grid and repeating the same line to the right edge. And the same procedure for
the top edge repeating the top edge line to the bottom edge of
the parallelogram. This closes the shape and
allows it to tile perfectly. Most tessellation artists use the term translation
instead of repetition. The outline here contains
two characters or motif as Escher called
them, a bug and a fish. Jason Panda is a
Canadian artist and school teacher in
Southern Ontario. I had no such luck when
I was a kid growing up to have an art
teacher that could do tessellations like this, His students are spoiled. He's done community
art projects such as street art
and installations. You can find more of his graphic style tessellations on Instagram and his website. Here's another example
from MC Escher number 128. It contains only
one motif , bird. The grid for this symmetry group can be arbitrarily drawn. Choose any easily
locatable point. In this case, I chose the tip of the beak. This creates
a square grid. If you look at
Escher's sketch below, this is also where he
chose to align the grid. The second image
follow the green line, the back edge of the bird tail. It links the top-left and the bottom left
corners of the grid with its simple arcs and repeats by translation all the
vertical segments of those squares in the grid. The orange line links the two top corners
of the grid and translates down to the bottom. Defines both the
top of the bird, the beak, head, neck, and body. On the other side of the line defines the belly and long legs. One must always remember to take into account both
sides of the line, the razor's edge, the perfect line that
defines both sides. Here's my re-creation of MC Escher's bird
tessellation number 128, built on top of a
grid of squares. It took me a while to get
all his proportions correct. Not too much neck, not too much tail, etc. The magic sentence for
this symmetry group P1, the group I like to
call up, down left, right is link with one line, the top-left corner to
the bottom left corner, and then link with
the second line, the top left to the
top right corner. Then repeat your lines up, down, / left, right to
close the shape. An important attribute here is that you can
stray if you wish. There are no mirrors here. Here's the bird with
the inside detail to that outline or perimeter
a bit of a jumble here. Till, till we add alternating colors
for every other bird. This helps to easily decipher the motif within
the tessellation. Let's figure this one out. Here. The grid is skewed. As long as opposite sides of
your grid remain parallel, your character will
tessellate using this method. We will look into
this skewed grid in video three of this series. For now, in KaleidoPaint. This is accomplished using a three finger gesture
on the screen. Again, the outline can be whichever group of fish
you decide to select, an arbitrary outline
as long as it encompasses the totality of
the different motifs of fish. Generally speaking, for
all 17 symmetry groups, your outline can contain
any number of items, characters, humanoids or
in this tessellation, fish bones from five
different fish species. Here is one of my tessellations, the original messy sketch from the older version of
KaleidoPaint in 2013. I was trying to allocate space
for all the doggy parts. The stamp itself
contains two characters. MC Escher has done over 30 different tessellations
in this symmetry group, but only five of these
had a single character. Don't let the outline of your tile restrain
you in any way. Use your imagination. The topics are endless, the perimeters are endless. The stamping grid
can be a square, rectangle, lozenge, rhombus. These four shapes all fall under the definition
of a parallelogram. You can skew your grid with three fingers in KaleidoPaint, stretch it in any direction. Some artists like to use
squares like in graph paper, that definitely makes it
easier to stamp a pattern. As soon as you skew your grid, it will square stamp easily
in only one direction. The other direction
will be repeated, but with an offset. The tile edge is
arbitrary here as well. It could follow the edge of any houses as long as it
encompasses them all. Or it could be a parallelogram
if you wanted to stamp it. This is another instance of
more than one character, item, thing, sketched within the tile. I'm not sure if it's
easier or more complex to have many items
within the perimeter. The discussion continues. Renée shows us a different way of creating tessellations
in this group. I never would have
thought to use a hexagon grid to start
design and it's beautiful. The tail just nestles between
the ears and the belly. Although her initial design
uses a hexagon once we reduce the perimeter of
the tile down two lines, it's easy to see that
the rule is still there. Tip of the tail, tail, Its back and up to the ear. That's the yellow line. The other line, the pink one, links the back paw on
the top of the tail. I repeat the magic sentence
for this symmetry group, You have two lines to draw. Link the top left
to the bottom left, then link the top left
to the top right, then translate your lines
up, down / left, right. In this case,
KaleidoPaint does it for you,
stray if you wish, as there are no mirrors Talking of straying away
from their rigid grid. How far does the
cat's tail wander? I've explored this in quite a few different
symmetry groups. It's like those
labyrinths games. when we were kids, finding the path from
start to finish. How far can you go the answer? Farrrr Let's have a look at the grid. I've chosen the left ear tip, then added red dots on these
and lines to connect them. Here, the whole of the
creature is contained within one section of the skewed
parallelogram grid. This is an example that
you can stray very far outside the perimeter of your grid with this
symmetry group. The simple up-down
left-right symmetry group can be not so
simple if you dare. Your lines connecting those
grid corners don't need to be complex like the ones
in the previous example, cat tails into the next galaxy. They can be quite simple. Whichever way you arrive at your final topic and placement. Either by sketching
the character then stretching it
to fit an outline, or by defining an outline and
fitting in your character. Both ways work and sometimes it's a mix
of both techniques. Here's another example
of a skewed grid. I call this tessellation
brain bucket duck. Here's the grid. Both lines, I repeat. Link the top-left
to the bottom-left, link the top-left, top-right. Then repeat your
lines up, down, left, right, and stray if you wish. Some outlines are complex. Others like in this seashell
tessellation are quite simple and the rules
can be bent slightly. The red line does not actually link top left to bottom left. It keeps on wandering
to join its own self. But the aqua segments saves
the day by closing the shape. Now I've given you a magic sentence, but by no means are
these rules rigid? They are simply tricks
to get you going. Look at this
tessellation by Henk. The back of the
saddle curving up defines the front of
the horse's nose. The ears nestle quite well
between belly and thigh. The rider's head and neck
beautifully define The back edge of the front leg. Wonderful use of
black and white, what they call positive
and negative space. The white rider is part of
the negative space around the black horse and vice
versa, alternating. Ben Marder is a new
acquaintance on social media. He has done wonderful
tessellations, check him out, follow
Penn wave on Instagram. Now that we've done
quite a few examples, you can probably spot
the grid by choosing an easily locatable element and noticing how it repeats
across the surface. I won't draw it out for you. I want you to hunt for
it and examine how the artist has nested all the
elements into each other. Very few artists keep the
grid absolutely square. This jerk tessellation by Alain Nicolas has a
slightly skewed grid. It's easy to spot it if you use the characters eyeball as
the corners of the grid. Neat how he has placed the
far foot around the nose, chin, chest, thumb and hand. Superbly done. Three elements, three motifs in this tessellation built
on a skewed grid. I've chosen the tip
of the fish's nose. it should be easy for you
now to spot the perimeter, the outline of those
three characters. There's a reference for
you in the sidebar. You can pause the video
and take your time. There are decisions to make like which instance to include, and how to assemble them
for your perimeter. Good practice while you
learn about tessellations. This is also by Alain Nicolas. It shows a perfectly square grid four motifs make up the
content of the tile, fish, butterfly,
hyena, and Phoenix. Can you spot the
outline of the stamp weaving its way in and
out of the square grid. The topics are endless
for tessellations, if we get our inspiration
from many places. Here I've seen the ovoid eye design in the bark
texture on birch trees. I've given you well
over a dozen examples of this p1 symmetry group. The one I like to
call the simple up-down / left-right
symmetry group. You should be on your way to
understanding this method and all of its newly
explained potential. In the next video, I will explain my long
time, no, see tessellation.
3. Long Time No See, a Tessellation from A to Z: Hello, I just want to show you how to create a grid
in symmetry group P1. In symmetry group P1. And if we turn it off or on, there is no grid in
this version anyhow. Now if we just draw a dot, you can see it's drawn
the corners of a grid. We can align those lines. That will give us our grid. Now in P1, it's a special
symmetry group that can skew the three finger
gesture like so. You can make it any
size grid you want. Lozenge, rhombus,
rectangle, or square. Once you're done, you can
always delete the grid. You can make it finer. Thickness. just so it doesn't interfere with
your creative process. Thickness go for the
thin guy. There we go. So one finger or stylus
is to draw a line. Like so. Two fingers to
navigate the screen. Zoom in, zoom out, or pan around. Three fingers to skew. If you want to draw a
line, with a stylus. If you want to fill a region, it has to be a closed region. You use a double-tap, like so, like so. That's it. This tessellation did
start off with a bit of an idea to stack my characters
one on top of each other, legs apart, standing on the shoulders of the
character below. A bit like Castell
building, human towers, the festivals in Spain. But then it all morphed
into another idea. I seem to follow the whims
of my intuition quite a bit. The basic grid behind this
symmetry group is as always, a parallelogram , a lozenge in this case, two pairs of
opposite parallel sides. I know, I know I said
I wouldn't use jargon. It just means either a square or rectangle or a
rhombus or diamond. Or lozenge As I have just explained. All that the grid
Lattice does is more or less tell you where to
place your drawing. You're in no way constrained
to stay within those lines. These are not mirrors like
in our previous classes. You may cross those lines. You're even encouraged
to stray far just like the cat into
the next galaxy. I wasn't too sure where to
place the arm and hand, but it seemed to fit quite well curling up towards
and around the shoe. Just like trying to
stuff something in the freezer when it
looks absolutely full. A little bit of
rearranging and you can usually find
some room, nudge, nudge there and you can slip
in the required appendage. Need to reshape the hands and feet keeping in mind as always, both sides of the line. He has weird slicked-up hair, but this is what takes up
the space between his legs. Trying to match the shoes
seen from different angles. It's not like a bilaterally
symmetrical character with a mirror down the middle. We need to draw all
the body parts here. Tweak on the jacket so it overlaps to the
front of the body. Some of these lines
affect the perimeter, the outline only slightly
some not. jacket, a bit dark for now, but this will be tweaked. Once we save and
recolor the tile, we will get into that
in another class. I've been using the
realign button under the symmetry menu all along
in this series of images, this is why the line of characters or a
bit on a diagonal. But there's nothing stopping you from leveling out the rows. Now let's rewind and take the tessellation back
to its two main lines. I may not have started drawing, sketching from the exact
corner of the lattice, but the final drawing can be reduced to just the
two main lines. After a bit of
recoloring Long time no see is a bit
easier to decipher. This is only my second
attempt at drawing a humanoid tessellation
in symmetry group P1. This simple up-down,
left-right method, the most simple of all. In this instance, I'm showing you a single extract of the
motif or character.
4. Similar Outlines — Radically Different Content: MC Escher created
this print entitled eight heads way before he knew anything about
tessellations. It was indeed plane or surface filling like
in tessellations. And did tile any size of surface with no
gaps or overlaps. I've outlined all eight
heads Escher arranged 4 right-side-up
and 4 upside down. And as I've mentioned before, the outline choice is arbitrary. You might see online
a different area selected or even the
pattern rotated. As long as the whole of
the design is selected. That will be the stamp, or in this case the
printing plate. Stamps can have any shape. This one has very simple edges. It depends what you place
inside the outline. Whereas tiles on the other hand are rectangular
geometric shapes. Eight characters within
this MC Escher tile. Here I'm tiling the
surface or plane using a cropped tile of that
first image we looked at. Keeping in mind here that MC Escher accomplished
this by hand. It lines up pretty well
to tile any size surface. Here's a quick series showing the drawing process
for Lean on Me. Also created in the
same symmetry group as MC Escher's eight heads. The original character
was boxed in tight in a slightly
skewed rectangle. Then a bit of intuition was allowed to peek
through to extend the helping hand
over the shoulder of the next instance
of the character. This is a good
example of the term, no overlaps in the
definition of tessellations. Purists using the
classic definition where it says no
overlaps and no gaps. Hand over the shoulder here
could be an illegal maneuver. What rules are
elastic sometimes, when it comes to
art, to solve this, you could simply outline the
tile in a different manner. Include the hand over,
the shoulder, as I have done with
the black outline. It's still a favorite, lots of empathy here. Now let's look at both
of these outlines, the base outline for MC Escher's eight heads and
the outline for Lean on Me. Eight characters
within the Escher tile and a single character
within the other tile, and it just blows me
away how the outline can be so similar
on these two tiles, but the topic so different. Both of these are simply wiggly, squarish shapes,
very simple edges. It's so depends on what you
can place inside the outline. The possibilities are endless. Escher used a square grid. Lean on Me is within a
slightly skewed grid. If you were lucky enough to have a class on tessellations
in school, you possibly
recognize those lines cut with a pair of scissors, a piece of cardboard taped to the other side
of your square. And the same maneuver done
for the top to the bottom. Sometimes there's a surprise
offset left, right? When dealing with
this symmetry group, it depends if you started with a rectangular grid
or a skewed grid, You haven't done anything wrong. It's the nature of
the symmetry group. If the rectangle is skewed, it will still tile
the plain perfectly, but will require an offset, one copying the Tile Vertically. The offset is a result of the original grid you had
when you started drawing? Not quite a 50/50
brick laying pattern. but similar in the
horizontal movement? This is when you can decide
as you export a drawing, if you will recolor the
tile itself once or save a large expanse of the drawing and
recolor each instance. The only time I
found this type of tile troublesome is when I was converting the
tile to vector, the alignment was a headache. Your choice. Once you truly start examining various
artist's tessellations, you might start to
see if their grids are perpendicular or skewed.
5. Rebuilding Pegasus, by M. C. Escher: MC Escher tessellated the winged horse of Greek
mythology, Pegasus. Let's examine how
this tessellation was built and try to
recreate it on our own. In order to make
the task easier, I've drawn a black
grid over top of a few instances to get a
feel for how the lines sway back and forth
over the tiles' edges to help in estimating where
they cross the tile's edges. The red square shows
one single tile. If you look at the yellow
line it connects the top left corner
to the bottom left, just like in the magic sentence. So I've given you.
The green line, also follows the rule. Connecting the top
left to the top right. I've repeated these lines of few times to show you the
perimeter of the tessellation. Here's my attempt at the
Pegasus nested shape using the KaleidoPaint App the red line connecting
the top-left, the bottom-left, the black line closing the shape by connecting the top left to the top right. What's nice about this
is that KaleidoPaint Does all that repeats for you. I am approximating the
color in Escher's Drawing. For the dark winged horse, KaleidoPaint
only recognizes one instance, so will allow you to
color only in one way. This version of the
drawing was recolored using Pixelmator on the iPad. I alternated the light
color with a dark color, both horizontally
and vertically. It makes it more
pleasing to look at. This is the original
MC Escher watercolor drawing from 1959. This is the traditional
way of coming up with a tessellation using
scissors and cardboard. I won't cover this technique in too much detail as there are dozens of videos on
YouTube about this. You can find them easily. But it is the way
I learned to do tessellations before
the age of the iPad.
6. Recap of the Magic Sentence for this Method : Four classes, four different
symmetry groups, you've learned quite
a bit more than many tessellation artists
around the globe. It seems some artists
find a method they like to use and
master it quite well, but then they stick to it. Nothing wrong with that. But to me, after a while the artwork seems
to look the same. I've challenged myself to learn all classic symmetry groups, all 17 of them. You can too master them all. To recap the symmetry group
P1 link with one line, the top left to the bottom left, and linked the top, left, the top right with another line. Then repeat your lines
up, down, left, right. Well, KaleidoPaint does this
part for you automatically. And of course I encourage you to stray way outside the
tile if you wish. Those aren't mirrors.
In the next class, we will take a short break and
explored the simplicity of creating patterns with
your new symmetry tricks. Patterns and tessellations
use the same rules. It's just the space
between that varies.
Francine Champagne, Tessellation Artist
