# Creating Symmetric Patterns Using MakeCode for Minecraft

We created this symmetric red, white and blue 50-block square pattern  in appreciation for U.S. Independence day. The left and right halves are mirror images as are the upper and lower halves.

For July 4th, we couldn’t resist making a red, white and blue pattern including one extra block TNT for a big bang (see YouTube video above).

Symmetric patterns are beautiful, fascinating and endlessly entertaining. Amazon lists 4,000 books on symmetry.  Wikipedia explores symmetry in mathematics,  biology, art, physics, chemistry, social interactions, architecture, poetry, quilts, rugs, physical attractiveness and music among other areas of human endeavor.

We created the MakeCode for Minecraft program described in this post just for the fun of it.  With the program, symmetric squares of any size (within reason) and using any number of Minecraft blocks can be created. The program user picks the Minecraft blocks to be used for the canvas, for the pattern and for the optional  border. The program first builds the background canvas for either one or two levels, then builds the pattern using the number of blocks specified by the user. Optionally, a border can be added.

We are amazed that such a simple program can create such beautiful patterns. Gazillions of combinations are possible, some more pleasing than others. Make your own.

## The Plan for the Symmetric Patterns Program

The plan for this symmetric patterns program is that it enable a user  to build a random, 4-way symmetric pattern in the following steps:

1. Specify Minecraft blocks in three lists; namely, canvasBlocks, patternBlocks and borderBlocks.
2. Use the on-chat command “canvas” to place one or two layers of blocks from the canvasBlocks list.
3. Use the on-chat command “pattern” to create a random, symmetric  pattern with blocks from the patternBlocks list.
4. The on-chat command “border” builds a simple border around the pattern using the first block in the borderBlocks list.

Details of the on-chat commands’ arguments are provided below in the description of the code. This table is a summary and handy when using the program.

## The MakeCode for Minecraft Code

### The on-start Block

The lists canvasBlocks, patternBlocks and borderBlocks are inputs to the program; that is, they can be changed to create different patterns.

Any number of blocks can be included in each list, but only the number specified in the on-chat commands will be used. I sometimes include more blocks than are used so that changing blocks can be done quickly with drag-and-drop. Because now the border can be only one block wide, only the first block is used; however, since I might add additional borders, it is specified as a list rather than a simple one-block variable.

### Canvas on-chat Command

The chat command arguments specify the size of the canvas and the number layers to be build. The top layer is even with the grass in a flat world. An optional underlayer can be specified, which is useful when glass blocks are the top layer.

The canvas on-chat command is implemented in three steps:

1. The two arguments are verified and, if out of range, set to default values.
2. The variable “center” is set to the player world position, but Y (the up/down coordinate) is set to the same as the grass. This variable is used as the reference point for building the canvas.
3. The canvas is built around center one  layer at a time in a loop. Each layer is built with a single fill block.

The argument num1 is the number of layers to build. num1 can have values 1 or 2, but also must not be greater than the number of blocks in the canvasBlocs list. If canvasBlocks contains no blocks, a white concrete block is added as the default.

The argument num2 is the size of the canvas specified as half of the final size. for example, if num2 is 80, the canvas will be 160 blocks square. Some limit is required because of the fill block limit volume is 32,768 blocks.

Canvas Code — Part 1 of 2 — Validate Arguments

If num1 and num2 are omitted on the command line, the defaults of 1 layer and 50 (100 square blocks) are used.

After the arguments are verified, the variable minusNum2 is calculated as the negative value of num2.

Next, the position variable center is calculated as coordinates X and Z being the same as the player world  position, but the Y coordinate is specified as 3, which is the same level as the grass in a flat world. Notice that the player need not be on the ground for center to be calculated correctly. By using this variable instead of player world position for later program actions, the reference is always the same even if the player moves. I often like to have my player at a high vantage point and moving around  so that I can see the action. I don’t want a program behaving erratically just because I move the player. For example, a fence built relative to player world position might be built, or partly built, in the air. Fixing a reference point like center solves that problem.

Canvas Code — Part 2 of 2 — Place 1 or 2 Layers Around Center.

The guts of the code is the loop on index variable Y_level that runs from 0 to num1 -1. If num1 (the number of levels) is 1, the loop only runs once. If it is 2, the loop runs twice.

The fill command uses the block at Y_Level in canvasBlocks; therefore, the top canvas level is the first block in canvasBlocks and the second block in canvasBlocks is the underlayer (the layer of blocks under the top level).

Each time through the loop, the Y coordinate for the from and to are the same, thus only a single layer of blocks are laid. The first pass through the loop, the top layer is set. The second pass, if any, the underlayer is set.

The from and to coordinates of the fill  block  define a square around the variable center as shown in the drawing below.

### Pattern on-chat Command

The size of the pattern and the number of blocks (num2) to be used are specified as chat command arguments. num1 is half the final square side. The pattern is left-right mirrored and upper-lower mirrored. It can also the thought of as a quarter of the final pattern rotated to each of the four quadrants.

The pattern on-chat code has three parts:

1. Validation of the parameters.
2. Setting the variable origin as the reference position. Then setting q1, q2, q3 and q4 as the lower left corner of each of the final quadrants.
3. Generating a random pattern of num2 blocks in quadrant 1, then mirroring it appropriately in quadrants 2, 3 and 4.

In pattern arguments, the size of the square (num1) that forms each of the quadrants of the final square must be positive. If zero or negative, it is set to default 5, which will result in a final square of 10 blocks. num2 is the number of blocks to be used, which must be at least 2. The patternBlocks list must have at least two blocks, the minimum number required to create a pattern.

Pattern Code — Part 1 of 3 — Argument Validation

After the arguments are validated the reference positions are set. origin is the set to the player’s initial world position except at grass level. q1, q2, q3 and q4 are set to the lower-left corner of each of the 4 quadrants, respectively.

q1 is set to origin. q2 is num1 blocks to the right (south)  of q1. q3 is num1 blocks west (below in drawing)  and num1 blocks south (right)  of q1. q4 is num1 blocks west (below in drawing) of q1.

Pattern Code — Part 2 of 3

The goal is to create a final square with four quadrants as shown here. I think of the upper-left quadrant as not mirrored with the other three quadrants mirrored as shown.

For each quadrant,  rows are thought of as starting at the lower left corner at  row 0, moving upward to row num1 – 1. Columns are thought of as starting at column 0, moving left to right to column num1-1.

Conceptually,  the pattern code strategy is to crate a pattern by loping through each row and column. For each (row, column) coordinate, a block is selected randomly form patternBlocks list. The selected block is then placed appropriately in each quadrant. In quadrant 1, the block is simply placed at position (row, column) relative to q1. In quadrant 2, the block is placed at (row, num1 -1 – column), which causes the placement to be the mirrored across the vertical boundary between the quadrants. The other two quadrants are similarly placed in mirror positions.

Pattern Code — Part 3 of 3

The drawing below is an illustration of the mirroring of quadrant 1 position (5, 6)

### Border on-chat Command

The border on-chat command calls the function “border” to do the work. It is implemented is a function so that it can be easily moved from one program to another.

After setting the reference point one block to the west and one block to the north of the lower-left corner of the large 4-quadrant square, the builder is employed to create a border around the square using the first block in borderBlocks list. The builder-algorithm is similar to that used my Builder Fence post.

Pattern Code — 3 of 3 — Mirror Quadrant 1 Random Pattern in Quadrants 2, 3 and 4.

## Get the Code

Symmetric Patterns  code is shared on Code Connection at this URL

https://makecode.com/_3C89FjDJaEbR

To get and use the code, follow these steps.

Click the Import button , which is upper right in the Code Connection window just below the banner. This will open the window shown below.

Click the Import URL button , which is on the right, to open the window shown below.

Paste the URL supplied for the program you want to use in the space under the text “Copy the URL …”

Click the Go ahead! button .

The next window you will see will be the MakeCode window with the code downloaded from the URL. At this point, you can treat it like any other code, e.g., run it, save it locally, modify it, publish your changes or whatever else your heat desires.

We have tested several other methods of downloading the code using the URL, for example, pasting the URL in a browser. No joy. For more detailed instruction see our post How to Use Shared MakeCode on Microsoft Code Connection for Minecraft.