003 • Response

puzzle_id:: 2-0ca9ddb6
description:: example_3
timestamp:: 24.357.081407
call_count:: 3
model:: gemini-2.0-flash-thinking-exp-1219

The user wants me to analyze example_3 of the current ARC task (2-0ca9ddb6) and formulate a natural language program.

Plan:

Describe the input and output grids of example_3.
Analyze the differences between the input and output grids using code, focusing on color changes and their locations relative to the original non-white pixels.
Check if the transformation rule hypothesized from the previous examples holds for this example.
Refine the natural language program if necessary to account for this new example.

Example 3 Analysis:

Input grid: 9x9, mostly white with single pixels of red (2), magenta (6), and blue (1). Output grid: 9x9, the red, magenta, and blue pixels remain. Yellow pixels appear around the red pixel, and orange pixels appear around the blue pixel. The magenta pixel does not have new pixels around it.

The transformation rule seems consistent: red pixels cause adjacent yellow pixels to appear, and blue pixels cause adjacent orange pixels to appear. Magenta pixels do not trigger any changes.

Observations and Impressions of Example 3:

The input grid is a 9x9 grid that is primarily white. There are three non-white pixels: a red pixel, a magenta pixel, and a blue pixel. The red pixel is located near the top-center, the magenta pixel is in the middle-right, and the blue pixel is near the bottom-center.

The output grid is also 9x9. The red, magenta, and blue pixels remain in their original locations. Around the red pixel, yellow pixels have appeared in the adjacent (up, down, left, right) cells. Around the blue pixel, orange pixels have appeared in the adjacent cells. The magenta pixel does not have any new colored pixels around it.

import numpy as np

input_grid = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0],
                       [0, 0, 0, 0, 0, 0, 0, 0, 0],
                       [0, 0, 2, 0, 0, 0, 0, 0, 0],
                       [0, 0, 0, 0, 0, 0, 0, 0, 0],
                       [0, 0, 0, 0, 0, 0, 0, 0, 0],
                       [0, 0, 0, 0, 0, 0, 6, 0, 0],
                       [0, 0, 0, 0, 0, 0, 0, 0, 0],
                       [0, 0, 0, 1, 0, 0, 0, 0, 0],
                       [0, 0, 0, 0, 0, 0, 0, 0, 0]])

output_grid = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0],
                        [0, 4, 0, 4, 0, 0, 0, 0, 0],
                        [0, 0, 2, 0, 0, 0, 0, 0, 0],
                        [0, 4, 0, 4, 0, 0, 0, 0, 0],
                        [0, 0, 0, 0, 0, 0, 0, 0, 0],
                        [0, 0, 0, 0, 0, 0, 6, 0, 0],
                        [0, 0, 0, 7, 0, 0, 0, 0, 0],
                        [0, 0, 7, 1, 7, 0, 0, 0, 0],
                        [0, 0, 0, 7, 0, 0, 0, 0, 0]])

input_colors, input_counts = np.unique(input_grid, return_counts=True)
output_colors, output_counts = np.unique(output_grid, return_counts=True)

print("Input grid dimensions:", input_grid.shape)
print("Output grid dimensions:", output_grid.shape)
print("Input color counts:", dict(zip(input_colors, input_counts)))
print("Output color counts:", dict(zip(output_colors, output_counts)))

changed_pixels = np.where(input_grid != output_grid)
print("Indices of changed pixels:", list(zip(changed_pixels[0], changed_pixels[1])))

input:
  width: 9
  height: 9
  colors:
    0: 78
    2: 1
    6: 1
    1: 1
  objects:
    - color: red
      position: (2, 2)
    - color: magenta
      position: (5, 6)
    - color: blue
      position: (7, 3)

differences:
  cells_changed: 7
  colors_changed:
    - white to yellow around red
    - white to orange around blue
  transformation:
    - for each red pixel in the input, add adjacent yellow pixels in the output.
    - for each blue pixel in the input, add adjacent orange pixels in the output.
    - magenta pixels do not trigger any changes.

Natural Language Program:

The input grid is a 9x9 grid. The color palette for this task includes white, blue, red, yellow, orange, and magenta.

Initialize the output grid by making an exact copy of the input grid.

Iterate through each cell in the input grid.

If a cell contains a red pixel (color value 2):

Identify the row and column coordinates of the red pixel.
In the output grid, change the color of the directly adjacent white pixels (those immediately above, below, to the left, and to the right) to yellow (color value 4). The original red pixel remains red in the output grid.

If a cell contains a blue pixel (color value 1):

Identify the row and column coordinates of the blue pixel.
In the output grid, change the color of the directly adjacent white pixels (those immediately above, below, to the left, and to the right) to orange (color value 7). The original blue pixel remains blue in the output grid.

Magenta pixels (color value 6) present in the input grid do not cause any changes to their adjacent pixels in the output grid. They remain magenta in the output grid.

time
response time	total elapsed
12.998	40.749

usage
token type	call count	total used
Prompt	7770	15167
Response	1534	5040
Total	9304	20207
Cached	0	0