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fix broken link; add morphic sequence images
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nmheim committed Feb 28, 2024
1 parent 89f3c05 commit 5808e8b
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8 changes: 5 additions & 3 deletions lectures/lecture03.md
Original file line number Diff line number Diff line change
Expand Up @@ -321,7 +321,7 @@ To visualize this sequence, we define the turning angles as follows:
$$\alpha_1(0)=\frac{7}{9}\pi,\quad\alpha_1(1)=-\frac{2}{9}\pi$$
The visualization for $w_{15}$ is depicted below:

![](../img/ex1.png){ style="width: 60%; margin: auto;" }
![](/img/morphic-sequence1.png){ style="width: 60%; margin: auto;" }

For the second example, we consider the morphism $\phi_2$ defined by
$$\phi(0) = 00,\quad \phi(1) = 101.$$
Expand All @@ -331,9 +331,11 @@ To visualize this sequence, we define the turning angles as follows:
$$\alpha_2(0)=\frac{5}{16}\pi,\quad\alpha_2(1)=-\frac{29}{60}\pi$$
The visualization for $w_{10}$ is depicted below:

![](../img/ex2.png){ style="width: 60%; margin: auto;" }
![](/img/morphic-sequence2.png){ style="width: 60%; margin: auto;" }

Now I will discuss generating these images in Racket using higher-order functions and currying. We will use the same turtle library as [before](../lecture01/#cb38-1) to draw the pictures. Thus our code starts with the following line:
Now I will discuss generating these images in Racket using higher-order functions and currying. We
will use the same turtle library as [before](lecture01#drawing-trees) to draw the pictures. Thus our
code starts with the following line:
```scheme
(require graphics/value-turtles)
```
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