Wow, thank you for the thumbs everyone. I really wasn't expecting that many! As a result, I now feel kind of obliged to share some of the details of the picture with anyone that might be interested:
I guess it probably took about 8 hours to design the picture and write the computer program to create it. The first couple of hours were spent on the artistic design:
I've always been rather interested in computationally / mathematically designed artwork, with a lot of M. C. Escher's prints falling into this category, in my mind. Of his pieces, things like his Circle Limit series (http://images.google.com/images?&q=escher+circle+limit) and Snakes woodcut (http://images.google.com/images?&q=escher+snakes) have always seemed very impressive. So, I guess it's pretty obvious where I got some of the inspiration for this piece from.
However, there were a couple of additional constraints I imposed on myself for this particular piece. In the Circle Limit's there are different orders of rotation at different points in a single print. E.g. in Circle Limit IV (one of my favourites), you'll see that the angels' feet always touch together in 3's, but angel wingtips always touch together in 4's. There are very good reasons for this in those prints, but this is not an effect I wanted carried over into the Tri-ominos picture. In Tri-ominos, you get a big bonus score for 6 pieces finally forming a solid hexagon, so I really wanted there to appear to be order-6 rotation at every point in the picture. On top of this, I didn't want any of the triangles to become too overtly stretched as Tri-ominos pieces are clearly equilateral triangles (all sides are the same length). Yes, obviously as my triangles reach the edges they're no longer equilateral, but they do fool the eye into thinking that they could be, but are just angled away from the viewer, as if wrapping over the surface of a sphere.
Talking of spheres, couldn't I have just created a sphere of Tri-omino pieces and rendered that? Again, it's not quite that simple. Equilateral triangles don't perfectly map arbitrarily onto a sphere - you'll notice in pictures of European footballs (http://images.google.com/images?&q=soccer+ball), for example, that the black and white design is formed from white hexagons (which would be perfect to break up into 6 Tri-omino pieces), but also from black pentagons - being 5-sided these don't form equilateral triangles when segmented, but are necessary to create that spherical shape for footballs.
So, anyway, with all that in mind it took a little while to come up with a mapping design I was relatively happy. In the final piece there are still some places that the eye suggests are incorrect 'dents' in the structure, but these are simply down to the above constraints I was imposing on myself, and my inability to find a better solution at the time.
So, onto the picture itself.
The Tri-omino pieces themselves are pretty simply rendered. I found that the Bold Arial Narrow font gave a number set that was pretty close to the one I have on my Tri-ominos pieces at home, so that's what I'm using there.
The background - I really didn't know what to do with that, so I ended up just going for that rather weak pseudo-marbled checkerboard (I thought dark blue contrasted against the cream yellow pieces relatively well).
As for the actual numbers on the pieces, the inner hexagon of pieces was a no-brainer, but I wanted the rest look relatively random, but without a clutter of similar pieces next to each other, and a sprinkle of trip's visible (i.e. not buried down at the sides too far where you wouldn't see them). I must have spent about 2 hours coming up with some numbers there that I was happy with. ... Sheesh, that's embarassing to think about!
And, anyway, so that's it. End result: what you see here. Just thought I'd share the process with you all.
And, just to finish, I just thought I'd give a nod to the only other Escher inspired image I've seen in my enormous 2 weeks on the site so far - Fidel Lainez's Arkham Horror picture:
And, just to finish, I just thought I'd give a nod to the only other Escher inspired image I've seen in my enormous 2 weeks on the site so far - Fidel Lainez's Arkham Horror picture:
Posted Sun Nov 25, 2007 1:47 pm
on the site so far - Fidel Lainez's Arkham Horror picture:
I guess it probably took about 8 hours to design the picture and write the computer program to create it. The first couple of hours were spent on the artistic design:
I've always been rather interested in computationally / mathematically designed artwork, with a lot of M. C. Escher's prints falling into this category, in my mind. Of his pieces, things like his Circle Limit series ( http://images.google.com/images?&q=escher+circle+limit) and Snakes woodcut ( http://images.google.com/images?&q=escher+snakes) have always seemed very impressive. So, I guess it's pretty obvious where I got some of the inspiration for this piece from.
However, there were a couple of additional constraints I imposed on myself for this particular piece. In the Circle Limit's there are different orders of rotation at different points in a single print. E.g. in Circle Limit IV (one of my favourites), you'll see that the angels' feet always touch together in 3's, but angel wingtips always touch together in 4's. There are very good reasons for this in those prints, but this is not an effect I wanted carried over into the Tri-ominos picture. In Tri-ominos, you get a big bonus score for 6 pieces finally forming a solid hexagon, so I really wanted there to appear to be order-6 rotation at every point in the picture. On top of this, I didn't want any of the triangles to become too overtly stretched as Tri-ominos pieces are clearly equilateral triangles (all sides are the same length). Yes, obviously as my triangles reach the edges they're no longer equilateral, but they do fool the eye into thinking that they could be, but are just angled away from the viewer, as if wrapping over the surface of a sphere.
Talking of spheres, couldn't I have just created a sphere of Tri-omino pieces and rendered that? Again, it's not quite that simple. Equilateral triangles don't perfectly map arbitrarily onto a sphere - you'll notice in pictures of European footballs ( http://images.google.com/images?&q=soccer+ball), for example, that the black and white design is formed from white hexagons (which would be perfect to break up into 6 Tri-omino pieces), but also from black pentagons - being 5-sided these don't form equilateral triangles when segmented, but are necessary to create that spherical shape for footballs.
So, anyway, with all that in mind it took a little while to come up with a mapping design I was relatively happy. In the final piece there are still some places that the eye suggests are incorrect 'dents' in the structure, but these are simply down to the above constraints I was imposing on myself, and my inability to find a better solution at the time.
So, onto the picture itself.
The Tri-omino pieces themselves are pretty simply rendered. I found that the Bold Arial Narrow font gave a number set that was pretty close to the one I have on my Tri-ominos pieces at home, so that's what I'm using there.
The background - I really didn't know what to do with that, so I ended up just going for that rather weak pseudo-marbled checkerboard (I thought dark blue contrasted against the cream yellow pieces relatively well).
As for the actual numbers on the pieces, the inner hexagon of pieces was a no-brainer, but I wanted the rest look relatively random, but without a clutter of similar pieces next to each other, and a sprinkle of trip's visible (i.e. not buried down at the sides too far where you wouldn't see them). I must have spent about 2 hours coming up with some numbers there that I was happy with. ... Sheesh, that's embarassing to think about!
And, anyway, so that's it. End result: what you see here. Just thought I'd share the process with you all.
And, just to finish, I just thought I'd give a nod to the only other Escher inspired image I've seen in my enormous 2 weeks
(please do correct me if there are others)