gpt4

---

I'm doing Prolog experiments.


The x and y coordinates represent a 0-indexed grid.


```prolog
% Example 0 input grid 12cols_17rows
object(input0_color8_x9_y0_width1_height1_mass1_shapePixel).
object(input0_color8_x7_y0_width1_height1_mass1_shapePixel).
object(input0_color8_x5_y0_width1_height1_mass1_shapePixel).
object(input0_color8_x1_y0_width1_height1_mass1_shapePixel).
object(input0_color2_x0_y10_width1_height1_mass1_shapePixel).
object(input0_color2_x0_y4_width1_height1_mass1_shapePixel).

% Example 0 output grid 12cols_17rows
object(output0_color8_x11_y10_width1_height7_mass7_shapeLine).
object(output0_color8_x9_y10_width1_height7_mass7_shapeLine).
object(output0_color8_x7_y10_width1_height7_mass7_shapeLine).
object(output0_color8_x3_y10_width1_height7_mass7_shapeLine).
object(output0_color8_x10_y4_width1_height6_mass6_shapeLine).
object(output0_color8_x8_y4_width1_height6_mass6_shapeLine).
object(output0_color8_x6_y4_width1_height6_mass6_shapeLine).
object(output0_color8_x2_y4_width1_height6_mass6_shapeLine).
object(output0_color8_x9_y0_width1_height4_mass4_shapeLine).
object(output0_color8_x7_y0_width1_height4_mass4_shapeLine).
object(output0_color8_x5_y0_width1_height4_mass4_shapeLine).
object(output0_color8_x1_y0_width1_height4_mass4_shapeLine).
object(output0_color2_x0_y10_width1_height1_mass1_shapePixel).
object(output0_color2_x0_y4_width1_height1_mass1_shapePixel).

% Example 1 input grid 10cols_14rows
object(input1_color8_x6_y0_width1_height1_mass1_shapePixel).
object(input1_color8_x2_y0_width1_height1_mass1_shapePixel).
object(input1_color2_x9_y11_width1_height1_mass1_shapePixel).
object(input1_color2_x9_y7_width1_height1_mass1_shapePixel).
object(input1_color2_x9_y3_width1_height1_mass1_shapePixel).

% Example 1 output grid 10cols_14rows
object(output1_color8_x3_y11_width1_height3_mass3_shapeLine).
object(output1_color8_x4_y7_width1_height4_mass4_shapeLine).
object(output1_color8_x0_y7_width1_height4_mass4_shapeLine).
object(output1_color8_x5_y3_width1_height4_mass4_shapeLine).
object(output1_color8_x1_y3_width1_height4_mass4_shapeLine).
object(output1_color8_x6_y0_width1_height3_mass3_shapeLine).
object(output1_color8_x2_y0_width1_height3_mass3_shapeLine).
object(output1_color2_x9_y11_width1_height1_mass1_shapePixel).
object(output1_color2_x9_y7_width1_height1_mass1_shapePixel).
object(output1_color2_x9_y3_width1_height1_mass1_shapePixel).

% Example 2 input grid 12cols_12rows
object(input2_color8_x0_y9_width1_height1_mass1_shapePixel).
object(input2_color8_x0_y6_width1_height1_mass1_shapePixel).
object(input2_color8_x0_y2_width1_height1_mass1_shapePixel).
object(input2_color2_x8_y11_width1_height1_mass1_shapePixel).
object(input2_color2_x4_y11_width1_height1_mass1_shapePixel).

% Example 2 output grid 12cols_12rows
object(output2_color8_x0_y9_width4_height1_mass4_shapeLine).
object(output2_color8_x4_y8_width4_height1_mass4_shapeLine).
object(output2_color8_x8_y7_width4_height1_mass4_shapeLine).
object(output2_color8_x0_y6_width4_height1_mass4_shapeLine).
object(output2_color8_x4_y5_width4_height1_mass4_shapeLine).
object(output2_color8_x8_y4_width4_height1_mass4_shapeLine).
object(output2_color8_x0_y2_width4_height1_mass4_shapeLine).
object(output2_color8_x4_y1_width4_height1_mass4_shapeLine).
object(output2_color8_x8_y0_width4_height1_mass4_shapeLine).
object(output2_color2_x8_y11_width1_height1_mass1_shapePixel).
object(output2_color2_x4_y11_width1_height1_mass1_shapePixel).
```


Think step by step, what are the transformations across all the examples, that goes from the input to the output.
With the following example, I want you to predict what the output should be


```prolog

% Example 3 input grid 17cols_12rows
object(input3_color8_x16_y10_width1_height1_mass1_shapePixel).
object(input3_color8_x16_y8_width1_height1_mass1_shapePixel).
object(input3_color8_x16_y5_width1_height1_mass1_shapePixel).
object(input3_color8_x16_y2_width1_height1_mass1_shapePixel).
object(input3_color2_x11_y11_width1_height1_mass1_shapePixel).
object(input3_color2_x6_y11_width1_height1_mass1_shapePixel).
object(input3_color2_x2_y11_width1_height1_mass1_shapePixel).

% Example 3 output grid 17cols_12rows
PREDICT the lines that starts with object(output3_
```
Repeat the previous example prolog code, with the PREDICT replaced with your predictions.

---

Based on the examples given, the transformation seems to follow a pattern:

- Every pixel object `color8` in the input generates several line objects `color8` in the output. The exact number, their coordinates, dimensions and mass depend on the orientation of the grid. 
- For grids oriented horizontally (12cols_17rows and 10cols_14rows), each input pixel generates a column of lines, with the height of each line and the gap between them increasing by one with each pixel from top to bottom. The last line's bottom coincides with the pixel's position.
- For grids oriented vertically (12cols_12rows), each input pixel generates a row of lines, with the width of each line and the gap between them increasing by one with each pixel from left to right. The last line's right end coincides with the pixel's position.
- The position of the lines depends on the pixel's position and the number of lines.
- The pixel objects `color2` are copied from the input to the output without change.

Applying these rules to the Example 3 input (17cols_12rows), which is vertically oriented, we get:

```prolog

% Example 3 input grid 17cols_12rows
object(input3_color8_x16_y10_width1_height1_mass1_shapePixel).
object(input3_color8_x16_y8_width1_height1_mass1_shapePixel).
object(input3_color8_x16_y5_width1_height1_mass1_shapePixel).
object(input3_color8_x16_y2_width1_height1_mass1_shapePixel).
object(input3_color2_x11_y11_width1_height1_mass1_shapePixel).
object(input3_color2_x6_y11_width1_height1_mass1_shapePixel).
object(input3_color2_x2_y11_width1_height1_mass1_shapePixel).

% Example 3 output grid 17cols_12rows
object(output3_color8_x16_y10_width1_height1_mass1_shapeLine).
object(output3_color8_x12_y9_width4_height1_mass4_shapeLine).
object(output3_color8_x8_y8_width4_height1_mass4_shapeLine).
object(output3_color8_x16_y8_width1_height1_mass1_shapeLine).
object(output3_color8_x12_y7_width4_height1_mass4_shapeLine).
object(output3_color8_x8_y6_width4_height1_mass4_shapeLine).
object(output3_color8_x16_y5_width1_height1_mass1_shapeLine).
object(output3_color8_x12_y4_width4_height1_mass4_shapeLine).
object(output3_color8_x8_y3_width4_height1_mass4_shapeLine).
object(output3_color8_x16_y2_width1_height1_mass1_shapeLine).
object(output3_color8_x12_y1_width4_height1_mass4_shapeLine).
object(output3_color8_x8_y0_width4_height1_mass4_shapeLine).
object(output3_color2_x11_y11_width1_height1_mass1_shapePixel).
object(output3_color2_x6_y11_width1_height1_mass1_shapePixel).
object(output3_color2_x2_y11_width1_height1_mass1_shapePixel).

```

Each `color8` pixel generates 3 `color8` lines with width 1, 4, 4 and the x-coordinate decreases by 4 each time. The `color2` pixels are copied as-is. The transformation for this vertical grid is different from the previous vertical grid, so it's likely there are more rules not covered by the examples, such as rules depending on grid size.

