001 • Response

puzzle_id:: 1-3aa6fb7a
description:: example_1
timestamp:: 24.356.195518
call_count:: 1
model:: gemini-2.0-flash-thinking-exp-1219

The user wants me to analyze the first example of an ARC task and formulate a natural language program describing the transformation from the input to the output grid.

Plan:

Describe the input grid: Identify its dimensions, the colors present, and any noticeable patterns or objects.
Describe the output grid: Identify its dimensions, the colors present, and any noticeable patterns or objects.
Identify differences: Compare the input and output grids to pinpoint the changes.
Formulate hypotheses: Based on the differences, propose potential transformation rules.
Develop a natural language program: Describe the transformation rule in a step-by-step manner.

Okay, let’s analyze the first example.

The input grid is 7x7. It contains white (0) pixels and azure (8) pixels. There appear to be two distinct ‘L’ shapes formed by the azure pixels.

The output grid is also 7x7 and contains white (0), azure (8), and blue (1) pixels. The azure ‘L’ shapes remain the same, but some white pixels adjacent to the azure shapes have turned blue.

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 shape:", input_grid.shape)
print("Input color counts:", input_colors)
print("Output grid shape:", output_grid.shape)
print("Output color counts:", output_colors)

diff_coords = np.where(input_grid != output_grid)
print("Coordinates of differences:", list(zip(diff_coords[0], diff_coords[1])))
print("Input values at diff:", input_grid[diff_coords])
print("Output values at diff:", output_grid[diff_coords])

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

differences:
  cells_changed: 2
  colors_changed:
    - from: white to blue
  transformation:
    - speculation: Fill adjacent white pixels to azure with blue

Natural Language Program:

Context: The input is a 7x7 grid containing white and azure pixels. There are two distinct ‘L’ shaped regions of azure pixels.
Initialization: Create a copy of the input grid as the starting point for the output grid.
Color Palette: The output grid will use white, azure, and blue pixels.
Transformation:
- Identify all azure pixels in the input grid.
- For each azure pixel, examine its immediate orthogonal (up, down, left, right) neighboring pixels.
- If a neighboring pixel is white and is the corner of an ‘L’ shape formed by the azure pixels, change the color of that white pixel to blue. Specifically, if an azure pixel at (r, c) has neighbors at (r-1, c) and (r, c-1) that are both white, or at (r-1, c) and (r, c+1) that are both white, or at (r+1, c) and (r, c-1) that are both white, or at (r+1, c) and (r, c+1) that are both white, then set those white neighbors to blue.
- More simply, find the white pixel orthogonally adjacent to an azure pixel that completes a 2x2 square of which the azure pixel is a corner. Change that white pixel to blue.

example_2

input

[[0 0 0 0 0 0 0]
 [0 0 0 0 0 8 0]
 [0 0 0 0 8 8 0]
 [0 8 8 0 0 0 0]
 [0 8 0 0 0 0 0]
 [0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0]]

output

[[0 0 0 0 0 0 0]
 [0 0 0 0 0 1 0]
 [0 0 0 0 8 8 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 0 0 0]]

images

time
response time	total elapsed
11.579	11.666

usage
token type	call count	total used
Prompt	2760	2760
Response	1459	1459
Total	4219	4219
Cached	0	0