# Baklava in Piet

Published on 30 April 2023 (Updated: 02 May 2023)

Welcome to the Baklava in Piet page! Here, you'll find the source code for this program as well as a description of how the program works.

## Current Solution

Baklava in Piet was written by:

• rzuckerm

• rzuckerm

If you see anything you'd like to change or update, please consider contributing.

## Introduction

Piet is an esoteric programming language. Esoteric programming languages make it difficult to implement even the simplest task, and this was my first foray into such languages. If that wasn't difficult enough, Piet is a graphical language, so you can't just pop into a text editor to create a program. Instead, you have to use an online editor to even create a program. To make things even more interesting, Piet uses a rotating color palette, where the color of the next instruction depends upon the current instruction. Finally, it is a stack-based language, so programming in it is akin to programming an old Hewlett-Packard calculator. If you'd like to learn more about the Piet language, see the Official Site.

Without further ado, let's dive in the implementation!

## High-Level Overview

This sample program implements Baklava using two main loops:

1. Output the top 10 lines:

• Output `n` spaces.
• Output `21 - 2*n` asterisks.
• Output a newline.

where `n` equals 1, 2, …, 10.

2. Output the bottom 11 lines:

• Output 21 asterisks.
• Output a newline.

then:

• Output `10 - floor(m / 2)` spaces.
• Output `m` asterisks.
• Output a newline.

where `m` equals 19, 17, …, 1.

If this is enough for you, then just jump to the Credits section. Otherwise, strap yourself in, and prepare for a very detailed description that goes through what each codel (code element) does.

## Very Detailed Description

ASCII characters need to be encoded as numbers. The following numbers are used:

• space: 32
• asterisk: 42
• newline: 10

Instructions are shown in the following format:

• X/Y coordinates of the program counter
• Instruction
• Stack contents

The direction pointer (DP), controls the flow of the program. The program starts at `(0, 0)`, and DP points to the right. When DP hits an edge or black cell, it rotates clockwise. The program terminates when there is nowhere to go.

White cells are considered to be no-ops (do-nothing instructions).

The program is divided into a number parts which are detailed in subsequent sections of this article. The parts are annotated with letters as follows:

Click here to open the diagram in a separate page so that you can refer back to it.

### Output Top 10 Lines (A thru G)

#### Space Loop Initialization (A)

`n = 10`:

``````( 0, 0): push 2  # 2
( 2, 0): push 5  # 2, 5
( 4, 0): mult    # 10 (n)
``````

`k = n`:

``````( 5, 0): dup     # 10 (n), 10 (k)
``````

#### Space Loop (B)

Output `" "`:

``````( 6, 0): push 4  # n, k, 4
(10, 0): dup     # n, k, 4, 4
(11, 0): mult    # n, k, 16
(12, 0): dup     # n, k, 16, 16
(13, 0): add     # n, k, 32
(14, 0): outc    # n, k
``````

`k = k - 1`:

``````(15, 0): push 1  # n, k, 1
(16, 0): sub     # n, k - 1
``````

Check whether the `k` is greater than `0` and branch accordingly:

``````(17, 0): dup     # n, k, k
(18, 0): push 1  # n, k, k, 1
(19, 0): not     # n, k, k, 0
(20, 0): gt      # n, k, 1 if k > 0 else 0
(21, 0): DP+     # n, k
``````

If `k` is greater than `0`, DP rotates clockwise, so a bunch of no-ops are executed, and the program goes back to the beginning of B. Otherwise, DP is unchanged, so the program continues on to the beginning of C.

#### Asterisk Loop Initialization (C)

Drop `k`:

``````(22, 0): pop     # n
``````

`m = 21 - 2 * n`:

``````(23, 0): dup     # n, n
(24, 0): push 1  # n, n, 1
(25, 0): not     # n, n, 0
(26, 0): push 1  # n, n, 0, 1
(27, 0): sub     # n, n, -1
(28, 0): mult    # n, -n
(29, 0): dup     # n, -n, -n
(30, 0): add     # n, -2 * n
(31, 0): push 3  # n, -2 * n, 3
(32, 1): push 7  # n, -2 * n, 3, 7
(34, 0): mult    # n, -2 * n, 21
(35, 0): add     # n, 21 - 2 * n (m)
``````

#### Asterisk Loop (D)

Output `"*"`:

``````(36, 0): push 3  # n, m, 3
(39, 0): dup     # n, m, 3, 3
(40, 0): add     # n, m, 6
(41, 0): dup     # n, m, 6, 6
(42, 0): dup     # n, m, 6, 6, 6
(43, 0): mult    # n, m, 6, 36
(44, 0): add     # n, m, 42
(45, 0): outc    # n, m
``````

`m = m - 1`:

``````(46, 0): push 1  # n, m, 1
(47, 0): sub     # n, m - 1
``````

Check whether `m` is greater than `0` and branch accordingly:

``````(48, 0): dup     # n, m, m
(49, 0): push 1  # n, m, m , 1
(50, 0): not     # n, m, m , 0
(51, 0): gt      # n, m, 1 if m > 0 else 0
(52, 0): DP+     # n, m
``````

If `m` is greater than `0`, DP rotates clockwise, so a bunch of no-ops are executed, and the program goes back to the beginning of D. Otherwise, DP is unchanged, so the program continues on to the beginning of E.

#### Output Newline (E)

Drop `m`:

``````(53, 0): pop     # n
``````

Output `"\n"`:

``````(54, 0): push 2  # n, 2
(55, 1): push 5  # n, 2, 5
(53, 3): mult    # n, 10
(52, 3): outc    # n
``````

#### Check If Last Line (F)

`n = n - 1`:

``````(51, 3): push 1  # n, 1
(50, 3): sub     # n - 1
``````

Check if `n` is greater than `0` and branch accordingly:

``````(49, 3): dup     # n, n
(48, 3): push 1  # n, n, 1
(47, 3): not     # n, n, 0
(46, 3): gt      # n, 1 if n > 0 else 0 (q)
(45, 3): not     # n, 1 - q
(44, 3): dup     # n, 1 - q, 1 - q
(43, 3): dup     # n, 1 - q, 1 - q, 1 - q
(42, 3): add     # n, 1 - q, 2 * (1 - q)
(41, 3): add     # n, 3 * (1 - q)
(40, 3): DP+     # n
``````

where:

``````3 * (1 - q) = 0 if n > 0 else 3
``````

If `n` is greater than `0`, DP is unchanged, so the program goes to the beginning of G. Otherwise, DP is rotated 3 steps clockwise, which is the same as 1 step counter-clockwise, so the program goes to the beginning of H.

#### Set Up For Next Iteration (G)

`k = n`:

``````(39,  3): dup     # n, k
``````

The program then executes a bunch of no-ops and goes back to the beginning of B.

### Output Bottom 11 Lines (H thru N)

#### Asterisk Loop Initialization (H)

Drop `n`:

``````(39, 4): pop     # empty
``````

Skip through a bunch of no-ops. Then, rotate DP 3 steps clockwise (1 step counter-clockwise):

``````( 4, 5): push 3  # 3
( 1, 5): DP+     # empty
``````

Skip through a no-op. Then, set `m = 21`:

``````( 0, 7): push 3  # 3
( 0, 8): push 7  # 3, 7
( 5, 7): mult    # 21 (m)
``````

`k = m`:

``````( 6, 7): dup     # m, k
``````

#### Asterisk Loop (I)

Output `"*"`:

``````( 7, 7): push 3  # m, k, 3
(10, 7): dup     # m, k, 3, 3
(11, 7): add     # m, k, 6
(12, 7): dup     # m, k, 6, 6
(13, 7): dup     # m, k, 6, 6, 6
(14, 7): mult    # m, k, 6, 36
(15, 7): add     # m, k, 42
(16, 7): outc    # m, k
``````

`k = k - 1`:

``````(17, 7): push 1  # m, k, 1
(18, 7): sub     # m, k - 1
``````

Check if `k` is greater than `0` and branch accordingly:

``````(19, 7): dup     # m, k, k
(20, 7): push 1  # m, k, k, 1
(21, 7): not     # m, k, k, 0
(22, 7): gt      # m, k, 1 if k > 0 else 0
(23, 7): DP+     # m, k
``````

If `k` is greater than `0`, DP rotates clockwise, so a bunch of no-ops are executed, and the program goes back to the beginning of I. Otherwise, DP is unchanged, so the program continues on to the beginning of J.

#### Output Newline and Check If Last Line (J)

Drop `k`:

``````(24, 7): pop     # m
``````

Output `"\n"`:

``````(25, 7): push 2  # m, 2
(27, 7): push 5  # m, 2, 5
(29, 7): mult    # m, 10
(30, 7): outc    # m
``````

`m = m - 2`:

``````(31, 7): push 2  # m, 2
(33, 7): sub     # m - 2
``````

Check if `m` is greater than `0` and branch accordingly:

``````(34, 7): dup     # m, m
(35, 7): push 1  # m, m, 1
(36, 7): not     # m, m, 0
(37, 7): gt      # m, 1 if m > 0 else 0
(38, 7): not     # m, 0 if m > 0 else 1
(39, 7): DP+     # m
``````

If `m` is greater than 0, DP is unchanged, so continue on to the beginning of K. Otherwise, DP is rotated clockwise, so go to the beginning of N.

#### Space Loop Initialization (K)

`n = 10 - floor(m / 2)`:

``````(40, 7): dup     # m, m
(41, 7): push 2  # m, m, 2
(43, 7): div     # m, floor(m / 2)
(44, 7): push 1  # m, floor(m / 2), 1
(45, 7): not     # m, floor(m / 2), 0
(46, 7): push 1  # m, floor(m / 2), 0, 1
(47, 7): sub     # m, floor(m / 2), -1
(48, 7): mult    # m, -floor(m / 2)
(49, 7): push 2  # m, -floor(m / 2), 2
(51, 7): push 5  # m, -floor(m / 2), 2, 5
(53, 7): mult    # m, -floor(m / 2), 10
(54, 7): add     # m, 10 - floor(m / 2) (n)
``````

#### Space Loop (L)

Output `" "`:

``````(55, 7): push 4  # m, n, 4
(59, 7): dup     # m, n, 4, 4
(60, 7): mult    # m, n, 16
(61, 7): dup     # m, n, 16, 16
(62, 7): add     # m, n, 32
(63, 7): outc    # m, n
``````

`n = n - 1`:

``````(64, 7): push 1  # m, n, 1
(65, 7): sub     # m, n - 1
``````

Check if `n` is greater than `0` and branch accordingly:

``````(66, 7): dup     # m, n, n
(67, 7): push 1  # m, n, n, 1
(68, 7): not     # m, n, n, 0
(69, 7): gt      # m, n, 1 if n > 0 else 0
(70, 7): DP+     # m, n
``````

If `n` is greater than `0`, DP is rotated clockwise, so a bunch of no-ops are executed, and the program goes back to the beginning of L. Otherwise, DP is unchanged, and the program continues on to the beginning of M.

### Setup For Next Line (M)

Drop `n`:

``````(71, 7): pop     # m
``````

`k = m`:

``````(71, 8): dup     # m, k
``````

After that a bunch of no-ops are executed, and the program goes back to the beginning of I.

#### Termination (N)

Drop `n`:

``````(40, 7): pop     # empty
``````

After that the program will terminate since there is nowhere else to go. I struggled with this, trying different shapes. Finally, the cross shape seemed to do the trick.

## Credits

The image for this article is based on a painting by Piet Mondrian called Victory Boogie-Woogie. He painted this in 1944 in expectation of victory in World War II. I chose this painting because its shape matches the output of the program. I copied it to the left and right just to fill in the empty spaces, and I think it looks cool!

## Thanks

Thanks to `alope107` for introducing me to the Piet esoteric language and for helping me fix a termination issue with this program (in other words, I couldn't get the silly thing to stop running!).

## How to Run the Solution

Go to the npiet interpreter site. On Linux, download `.tar.gz` and extract the contents. Follow the instructions in the `README` file. On Windows, download the `.zip` file and extract the contents. Follow the instructions in the `README` file.

To run the code, use this:

``````npiet baklava.png
``````

Alternatively, you can go to the Online Piet Editor and Interpreter site, import `baklava.png`, and execute it.