commit 0db35cad5429ea6ec84b69018603be09ce6a25fb
parent ad8e61ee2f6fda16656b61c5f23268bc41e88ee9
Author: mpizzzle <m@michaelpercival.xyz>
Date: Sat, 7 Nov 2020 14:28:13 +0000
minor formatting
Diffstat:
3 files changed, 10 insertions(+), 11 deletions(-)
diff --git a/2020.html b/2020.html
@@ -32,9 +32,10 @@
<h2 id='penrose-tilings-part-1'>Penrose Tilings part 1</h2>
<small>[<a href='#penrose-tilings-part-1'>link</a>—<a href='blog/penrose-tilings-part-1.html'>standalone</a>]</small>
<p>I recently read an article that <a href="https://www.nobelprize.org/prizes/physics/2020/penrose/interview/">Roger Penrose</a> won a nobel prize for his theoretical work on Black Holes, which I'm sure is well deserved. Another creation of Roger Penrose, 'Penrose tilings' are also very interesting, being his solution for tiling an infinite plane aperiodically with only two tiles. Penrose tilings have an Escheresque quality to them (Escher and Penrose famously were both inspired by one-another during their respective careers) which I find fascinating.</p>
-<p>Having just moved into a new (tragically empty) flat, I've been inspired to try decorating it with some self created art, and Penrose tiling's beauty in conjunction with their relative ease of computability make them an ideal candidate. The idea I have is to write a program to generate some basic Penrose tilings, where I can then play around with the colour scheme, print out a frame, and paint by hand in an Escher like style. How is that going to work? Let's find out.</p>
+<p>Having just moved into a new (tragically empty) flat, I've been inspired to try decorating it with some self created art, and Penrose tiling's beauty in conjunction with their relative ease of computability make them an ideal candidate. The idea I have is to write a program to generate some basic Penrose tilings, where I can then play around with the colour scheme, print out a frame, and paint them by hand in an Escher like style. How is that going to work? Let's find out.</p>
-<p>The rules for constructing penrose tilings are well documented, <a href="https://tartarus.org/~simon/20110412-penrose/penrose.xhtml">this</a> link in particular explains the iterative process in better detail than I ever could. The initial starting triangle shares it's geometry with a decagon (I will refer to this triangle type as 't123'). The easiest way to construct it is to draw a line of length 1, rotate it by π/5 radians with respect to the origin; optionally repeat nine times and you have a decagon. Conveniently (0, 0) is the middle of the screen when it comes to computer graphics, so arranging the triangles around the center is trivial. The simplest method is to start by taking each t123 triangle and dividing it into three sub triangles; you can calculate their geometry by finding two new vertices along the parent t123 triangle using the golden ratio. Doing this correctly you can fit two triangles of type t123 and one of t124 perfectly into the parent t123 triangle, and in a similar manner the rules for dividing t124 triangles is to fit one t123 and one t124. Boom, infinite Penrose tilings. Simple right? Check out the initial decagon and first t123 split below:
+<p>The rules for constructing penrose tilings are well documented, <a href="https://tartarus.org/~simon/20110412-penrose/penrose.xhtml">this</a> link in particular explains the iterative process in better detail than I ever could.</p>
+<p>The initial starting triangle shares it's geometry with a slice from a decagon (I will refer to this triangle type as 't123'). The easiest way to construct it is to draw a line of length 1, rotate it by π/5 radians with respect to the origin; optionally repeat nine times and you have a decagon. Conveniently (0, 0) is the middle of the screen when it comes to computer graphics, so arranging the triangles around the center is trivial. The simplest method is to start by taking each t123 triangle and dividing it into three sub triangles; you can calculate their geometry by finding two new vertices along the parent t123 triangle using the golden ratio. Doing this correctly you can fit two triangles of type t123 and one of t124 perfectly into the parent t123 triangle, and in a similar manner the rules for dividing t124 triangles is to fit one t123 and one t124. Boom, infinite Penrose tilings. Simple right? Check out the initial decagon and first t123 split below:
<p><img src="blog/assets/pizza.png" alt="" width="540" height="540" />
<img src="blog/assets/more_complicated_pizza.png" alt="" width="540" height="540" /></p>
@@ -79,7 +80,7 @@
<p>I know there are better and more elegant ways of shading Penrose tilings but I feel happy that I've done what I set out to do, now the hard part is waiting for divine inspiration to kick in before I try and paint one for real.</p>
<p>Peace out.</p>
-<small>Sat, 07 Nov 2020 14:12:33 +0000</small>
+<small>Sat, 07 Nov 2020 14:26:36 +0000</small>
</div>
<div class='entry'>
<h2 id='on-shaders'>on shaders</h2>
diff --git a/blog/penrose-tilings-part-1.html b/blog/penrose-tilings-part-1.html
@@ -8,9 +8,10 @@
<h1>Penrose Tilings part 1</h1>
<small>[<a href='../2020.html#penrose-tilings-part-1'>link</a>—<a href='penrose-tilings-part-1.html'>standalone</a>]</small>
<p>I recently read an article that <a href="https://www.nobelprize.org/prizes/physics/2020/penrose/interview/">Roger Penrose</a> won a nobel prize for his theoretical work on Black Holes, which I'm sure is well deserved. Another creation of Roger Penrose, 'Penrose tilings' are also very interesting, being his solution for tiling an infinite plane aperiodically with only two tiles. Penrose tilings have an Escheresque quality to them (Escher and Penrose famously were both inspired by one-another during their respective careers) which I find fascinating.</p>
-<p>Having just moved into a new (tragically empty) flat, I've been inspired to try decorating it with some self created art, and Penrose tiling's beauty in conjunction with their relative ease of computability make them an ideal candidate. The idea I have is to write a program to generate some basic Penrose tilings, where I can then play around with the colour scheme, print out a frame, and paint by hand in an Escher like style. How is that going to work? Let's find out.</p>
+<p>Having just moved into a new (tragically empty) flat, I've been inspired to try decorating it with some self created art, and Penrose tiling's beauty in conjunction with their relative ease of computability make them an ideal candidate. The idea I have is to write a program to generate some basic Penrose tilings, where I can then play around with the colour scheme, print out a frame, and paint them by hand in an Escher like style. How is that going to work? Let's find out.</p>
-<p>The rules for constructing penrose tilings are well documented, <a href="https://tartarus.org/~simon/20110412-penrose/penrose.xhtml">this</a> link in particular explains the iterative process in better detail than I ever could. The initial starting triangle shares it's geometry with a decagon (I will refer to this triangle type as 't123'). The easiest way to construct it is to draw a line of length 1, rotate it by π/5 radians with respect to the origin; optionally repeat nine times and you have a decagon. Conveniently (0, 0) is the middle of the screen when it comes to computer graphics, so arranging the triangles around the center is trivial. The simplest method is to start by taking each t123 triangle and dividing it into three sub triangles; you can calculate their geometry by finding two new vertices along the parent t123 triangle using the golden ratio. Doing this correctly you can fit two triangles of type t123 and one of t124 perfectly into the parent t123 triangle, and in a similar manner the rules for dividing t124 triangles is to fit one t123 and one t124. Boom, infinite Penrose tilings. Simple right? Check out the initial decagon and first t123 split below:
+<p>The rules for constructing penrose tilings are well documented, <a href="https://tartarus.org/~simon/20110412-penrose/penrose.xhtml">this</a> link in particular explains the iterative process in better detail than I ever could.</p>
+<p>The initial starting triangle shares it's geometry with a slice from a decagon (I will refer to this triangle type as 't123'). The easiest way to construct it is to draw a line of length 1, rotate it by π/5 radians with respect to the origin; optionally repeat nine times and you have a decagon. Conveniently (0, 0) is the middle of the screen when it comes to computer graphics, so arranging the triangles around the center is trivial. The simplest method is to start by taking each t123 triangle and dividing it into three sub triangles; you can calculate their geometry by finding two new vertices along the parent t123 triangle using the golden ratio. Doing this correctly you can fit two triangles of type t123 and one of t124 perfectly into the parent t123 triangle, and in a similar manner the rules for dividing t124 triangles is to fit one t123 and one t124. Boom, infinite Penrose tilings. Simple right? Check out the initial decagon and first t123 split below:
<p><img src="assets/pizza.png" alt="" width="540" height="540" />
<img src="assets/more_complicated_pizza.png" alt="" width="540" height="540" /></p>
diff --git a/rss.xml b/rss.xml
@@ -16,9 +16,10 @@ Updates from Michael Percival. Give this file to your RSS feeder to receive blog
<pubDate>Sat, 07 Nov 2020 14:12:33 +0000</pubDate>
<description><