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    Lab 13: Part 2: Recursive Graphics
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@section('content')

# Lab 13: Part 2: Recursive Graphics

## Task 0. Study template file
Open `lab11/recursiveGraphics.py` and study the provided box function:

```py
def box(x, y, size, color1, canvas):
    b = Rectangle(size, size, Point(x, y))
    b.setFillColor(color1)
    canvas.add(b)
```

This function draws a single box (Rectangle) of side length `size`, centered at `(x, y)`, filled with the color `color1`. The resulting box is added to the given cs1graphics Canvas (`canvas`).

This function is then tested in the main block:
```py
if __name__ == '__main__':

	# TEST FUNCTIONS HERE

	labcanvas = Canvas(500, 500, 'ivory', 'Example 1')
	box(100, 160, 200, 'green', labcanvas)
	box(300, 250, 200, 'red', labcanvas)
	box(50, 350, 75, 'blue', labcanvas)
```

Producing a graphic that looks like this:
<img src="box.png" style="max-width:500px">


## Task 1. nested boxes
Write a recursive function `makeNestedBoxes(x, y, size, color1, color2, canvas)` that produces nested boxes of alternating colors.

The largest box is drawn first, filled with `color1`, and then the next box has a side length that is 10 smaller and is filled with `color2`, etc.

This pattern continues as long as the size of the box is greater than 10.

Your `makeNestedBoxes` function must be <span class="note">recursive</span>.

<img src="nestedBoxes.png" style="max-width:500px">


Invocations to test your nested boxes:
```py

if __name__ == '__main__':
    task2canvas = Canvas(500, 500, 'darkolivegreen')
    makeNestedBoxes(200, 400, 100, 'red', 'ivory', task2canvas)
    makeNestedBoxes(150, 100, 200, 'purple', 'gold', task2canvas)
    makeNestedBoxes(400, 200, 180, 'navy', 'lightskyblue', task2canvas)
```


## Task 2. box pattern

Building upon the `makeNestedBoxes` function above, this task adds smaller versions of nested boxes at each of the four corners of every box.

The ratio of a box size to the corner box size is 1:3.  The corner boxes can only be drawn when they have a size greater than or equal to 10. Your `nestedBoxPattern` function must be **recursive**.

Hint: start with only one corner box (e.g. upper left), and when that works, go back and add in the
other 3 corner boxes.

<img src="navyboxes.png" style="max-width:500px">

<img src="pink.png" style="max-width:500px">


The patterns above were generated by the following code:

```py
if __name__ == '__main__':

    paper2 = Canvas(600, 600, 'white', 'paper2')
    nestedBoxPattern(300, 300, 400, 'navy', 'ivory', paper2)

    paper3 = Canvas(1500, 1500, 'black', 'paper3')
    nestedBoxPattern(750, 750, 500, 'deeppink', 'slategray', paper3)
```

`nestedBoxPattern` takes 6 parameters:

1. the `x` and `y` point where the box is centered
2. the `size` of the largest box
3. the outermost `color1`,
4. the alternating `color2`
5. the `Canvas` where the drawing should appear

Here is a [chart of available cs1graphics colors](../lab01/colors)

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