Eight Spiraling Cubes

"Eight Spiraling Cubes"
Compass and straightedge, pencil and Mahogany ink on paper.
Oct x-Nov 10, 2013
AA13


This drawing contains no real curves, only straight lines. Each cube is embedded inside the other as they turn inwards becoming ever so smaller. Is this two-dimensional figure possible in three dimensions?
Unsure on how to answer that myself, I thought I would instead share a few process sketches, and  a couple of heart-felt thoughts I wrote down during the different windows of time I spent creating this piece.



October 12: "Just when I had thought a drawing would be so simple, I find myself working on the biggest challenge I have ever attempted. It is so hard, to the point where I start to think I just won't be able to do it, and I seriously consider giving up.
But then, a sort of creative curiosity kicks in: how would I ever find out if this seemingly impossible endeavor is simply out of reach altogether, or if it is just a little further than I could imagine?"



October 12: "The world is resplendent with order and beauty. To this we are all still beginners, as there are infinite further layers of significance to unveil"



November 6: "Life is the unending work in progress"

Hey, thanks for lending an ear!
;)



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3D Fractal Geometric Drawings: Icosahedral / Dodecahedral Stars

"Dodecahedral Star"
Fractal geometric drawing; arrangement of (3D) Dodecahedra
in the Pythagorean Lute (from subdivisions of a Pentagon/Pentacle)
drawn by hand using classic geometric construction. No computer, pre-existing image or measurements were used to create this drawing.
Compass and straightedge, pencil and ink on archival paper.
Alberto J. Almarza
September 1, 2013
























"Icosahedral Star"
Fractal geometric drawing; arrangement of (3D) Icosahedra
(from  subdivisions of a Hexagon; incremental tilling -or fractal tessellation-)
drawn by hand using classic geometric construction. No computer, pre-existing image or measurements were used to create this drawing.
Compass and straightedge, pencil and ink on archival paper.
Alberto J. Almarza
September 18, 2013





Thanks for visiting!
Please feel free to post questions or comments!


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Triangulated (Golden Sphere) Polyhedron

Compass + straightedge sphere construction. Pencil, Walnut and Caoba ink on paper
Alberto J. Almarza
Created May 30, 2013
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Machinarum Mundi Automata

"Machinarum Mundi Automata"
Pencil, Walnut ink, tea and watercolor on board
Alberto J. Almarza
Created March 28, 2013
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Anamorphic Vessel Drawing

So during class, I told my 7th grade students:

"I was working on this drawing of a floating vessel, and I worked so hard on making it so realistic that when I finished the drawing, it actually floated off the page!"

They were immediately skeptic, but deeply curious, as I've been known to say crazy things like that, which turn out somehow to be true (sometimes my job as an art teacher is to spark a kid's imagination and sense of enthusiasm about the world, perhaps at the expense of a little healthy dose of exaggeration!)

"What, you don't believe me?" I said, "take a look at this..."




"?!... how did you do that?"

I made this "Torisian Vessel" with compass and straightedge, using a technique called "anamorphosis". In this case, it involves a common two dimensional drawing that has been "stretched" along the surface of the paper. As a result of foreshortening and perspective, when seen from a certain angle the drawing is reconstituted and appears to be three dimensional.

This is what the drawing actually looks like when viewed "straight":



As I usually do with projects of a more technical nature, I began by doing process sketches and studies. I first had to teach myself how to distort an image for the right effect, so after getting some more Da Vinci, Durer and Holbein into my brain, I started simple by attempting an anamorphic sphere.

       

Even though it was not perfect, the anamorphic sphere sketch was good enough to at least encourage me to go a bit further. I begun doing process for the vessel idea, which in turn was informed and inspired by older notes from 2011.

The key challenge became to understand and translate the details of an image from a simple square grid into a distorted, stretched grid.
I arrived at a final draft, which just needed some corrections, but for the most part seemed to have worked.

     

Then it wasn't for another couple of months or so that I finally drew the final piece, which I finished by adding some walnut ink and watercolor.



To check out a cool little 2 minute music clip about this drawing, click here.

Hope you enjoyed!
See you next time.



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Sphere Made of Cubes Made of Triangles

"Six Trajectories of Time Space"
Sphere made of cubes made of triangles.
Compass and straightedge, pencil and ink on paper.
February 2, 2013
Alberto J. Almarza
AA13

Watch a frame by frame clip of the making of this sphere.

To me, the real magic of this drawing ("magic" which I don't take credit for: it's just the geometric nature of things!) is that this 3-dimensional sphere -and infinite other forms- can emerge from something as simple as a grid of triangles. I call this grid "Hexagrid", but you know, it probably has a real name somewhere out there in math.


How many triangles do you see in this image? If you look close enough, I say a whole bigillion of them, right?
Can you see the cubes? They are EVERYWHERE, in different sizes, going in six directions at once: up, down, forward, backward and side to side!

But in order to be able to visualize this drawing fully, I first had to  be in the proper frame of mind...

Well, it all began with Minecraft.

Yes, I am a 31 year old, grown man, and I play Minecraft!
My excuse is that I have an 8 year old son who I play with, but mostly that the game is frickin AWESOME, specially for creative types! Excellent way to waste my time! :]
Though I am tempted to tell you all about Minecraft and our "creations", I'll just tell you the short story.

After we built -block by block- our Castle in the Sky Maze (complete with traps, riddles and secret treasure chambers) we were ready for a new challenge. We had a lot of fun making the towers; trying to make them round.

 You see, round things in Minecraft are not all that simple at first, because the game is pixel-based, so all objects are cubes. I became excited about this idea of making circles (no news) but this time in minecraft. 

How do we get circles out of squares, and spheres out of cubes?

To this endeavor we dedicated a whole new world: a world in progress I called Radiolarian Garden Sculpture Park, which I may show you one day (if I don't completely guilt trip myself out of playing minecraft first...)

You know when you do something for a bit too long... and then you start seeing it everywhere? and, are you obsessive like me?
Well, working on this world I started thinking/drawing about circles and squares and cubes and spheres...

    

and then, WOW,  it suddenly hit me: 

It is possible to draw two-dimensional representations of three-dimensional spheres made of isometric cubes derived from regular hexagons made of equilateral triangles!!! Whaa?!

(It was one of those excellent moments of like: "I'm a total dork. But i dont car.")



And that's the end of the story of that drawing.
Hope you enjoyed!
Thanks for visiting!




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