001 • Response

puzzle_id:: 1-3aa6fb7a
description:: example_1
timestamp:: 24.357.081407
call_count:: 1
model:: gemini-2.0-flash-thinking-exp-1219

The user wants me to analyze an example pair of input and output grids from an ARC task. I need to observe the grids, identify differences, and formulate a natural language program that describes the transformation from input to output.

Plan:

Perceptual Description: Describe the input and output grids verbally.
Code Examination: Use code to extract grid information (dimensions, colors, object properties, differences).
YAML Documentation: Capture key information about the input and differences in YAML format.
Transformation Rule (Hypothesis): Based on the observations, propose a preliminary natural language description of the transformation.
Natural Language Program: Refine the transformation rule into a detailed natural language program.

The input grid contains an ‘azure’ (8) object that resembles a sideways ‘L’ shape in the top-left and bottom-right. The background is ‘white’ (0). The output grid is nearly identical to the input, except that two ‘white’ (0) pixels adjacent to the ‘azure’ (8) object have been changed to ‘blue’ (1).

import numpy as np
from collections import Counter

input_grid = np.array([[0, 0, 0, 0, 0, 0, 0],
                       [0, 8, 0, 0, 0, 0, 0],
                       [0, 8, 8, 0, 0, 0, 0],
                       [0, 0, 0, 0, 8, 8, 0],
                       [0, 0, 0, 0, 0, 8, 0],
                       [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, 8, 1, 0, 0, 0, 0],
                        [0, 8, 8, 0, 0, 0, 0],
                        [0, 0, 0, 0, 8, 8, 0],
                        [0, 0, 0, 0, 1, 8, 0],
                        [0, 0, 0, 0, 0, 0, 0],
                        [0, 0, 0, 0, 0, 0, 0]])

input_colors = Counter(input_grid.flatten())
output_colors = Counter(output_grid.flatten())

print("Input Grid Analysis:")
print(f"  Dimensions: {input_grid.shape}")
print(f"  Color counts: {input_colors}")

print("\nOutput Grid Analysis:")
print(f"  Dimensions: {output_grid.shape}")
print(f"  Color counts: {output_colors}")

diff_coords = np.where(input_grid != output_grid)
changed_pixels = list(zip(diff_coords[0], diff_coords[1]))
print("\nDifferences:")
print(f"  Number of cells changed: {len(changed_pixels)}")
print("  Coordinates of changed pixels (input -> output):")
for r, c in changed_pixels:
    print(f"    ({r}, {c}): {input_grid[r, c]} -> {output_grid[r, c]}")

input:
  width: 7
  height: 7
  colors:
    0: 45
    8: 6
  objects:
    - color: azure
      shape: L-like
      positions: [(1, 1), (2, 1), (2, 2), (3, 4), (3, 5), (4, 5)]

differences:
  cells_changed: 2
  colors_changed:
    - white to blue
  transformation:
    - Adjacent white pixels to the azure object are changed to blue.
    - The change seems to occur at the concave corners of the azure 'L' shape.

Natural Language Program:

The input grid is a 7x7 grid primarily filled with ‘white’ (0) pixels. There is a single ‘azure’ (8) object formed by a contiguous block of pixels, resembling a sideways ‘L’ shape made of two segments. The first segment is vertical in the top-left, and the second is horizontal in the bottom-right.

To create the output grid, start with a copy of the input grid. Identify the ‘azure’ (8) object. Locate the ‘white’ (0) pixels that are directly adjacent (horizontally or vertically) to the ‘azure’ (8) object, specifically those that fill the concave corners of the ‘L’ shape. Change the color of these adjacent ‘white’ (0) pixels to ‘blue’ (1). The color palette for the output grid includes ‘white’ (0), ‘blue’ (1), and ‘azure’ (8).

time
response time	total elapsed
9.486	9.57

usage
token type	call count	total used
Prompt	2309	2309
Response	1164	1164
Total	3473	3473
Cached	0	0