002 • History

puzzle_id:

2-0ca9ddb6

description:

example_2

timestamp:

24.356.195518

call_count:

2

Begin puzzle: 2-0ca9ddb6

example_1

input

[[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 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 1 0 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 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 7 0 0]
 [0 0 0 0 0 7 1 7 0]
 [0 0 0 0 0 0 7 0 0]
 [0 0 0 0 0 0 0 0 0]]

images

../../../../_images/000-example_1_input15.png ../../../../_images/000-example_1_output15.png

observations

The user wants me to analyze the first example pair of an ARC task. I need to describe the input and output grids, use code to extract relevant information, and then formulate a natural language program explaining the transformation.

Input Grid Analysis:

  • The input grid is 9x9.

  • It contains white (0), red (2), and blue (1) pixels.

  • There is a single red pixel and a single blue pixel.

Output Grid Analysis:

  • The output grid is also 9x9.

  • It contains white (0), red (2), blue (1), yellow (4), and orange (7) pixels.

  • The red and blue pixels remain in their original positions.

  • Yellow pixels appear around the red pixel.

  • Orange pixels appear around the blue pixel.

Transformation Hypothesis: It seems like the colors around the single colored pixels are changed based on the color of the central pixel.

Okay, let’s analyze the first example.

The input grid is a 9x9 grid with mostly white pixels. There is a single red pixel located at (3, 2) (row index, column index) and a single blue pixel located at (6, 6).

The output grid is also a 9x9 grid. The red pixel remains at (3, 2) and the blue pixel remains at (6, 6). Surrounding the red pixel, the adjacent white pixels (horizontally, vertically, and diagonally) have become yellow. Surrounding the blue pixel, the adjacent white pixels have become orange.

import numpy as np
from collections import Counter

input_grid = np.array([[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, 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, 1, 0, 0],
                       [0, 0, 0, 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, 0],
                        [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, 7, 0, 0],
                        [0, 0, 0, 0, 0, 7, 1, 7, 0],
                        [0, 0, 0, 0, 0, 0, 7, 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 Color Counts:", input_colors)
print("Output Color Counts:", output_colors)

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

input:
  width: 9
  height: 9
  colors:
    0: 79
    1: 1
    2: 1
  objects:
    - color: red
      position: (3, 2)
    - color: blue
      position: (6, 6)

output:
  width: 9
  height: 9
  colors:
    0: 69
    1: 1
    2: 1
    4: 4
    7: 3
  objects:
    - color: red
      position: (3, 2)
    - color: blue
      position: (6, 6)
    - color: yellow
      positions: [(2, 1), (2, 3), (4, 1), (4, 3)]
    - color: orange
      positions: [(5, 6), (6, 5), (6, 7), (7, 6)]

differences:
  cells_changed: 10
  colors_changed: white to yellow around red, white to orange around blue
  transformation:
    - Identify single red pixel.
    - Change adjacent white pixels to yellow.
    - Identify single blue pixel.
    - Change adjacent white pixels to orange.

Natural Language Program:

The input grid is a 9x9 grid containing single isolated red and blue pixels on a white background.

To create the output grid:

  1. Start with the input grid.

  2. Locate the single red pixel.

  3. Change the color of the immediately adjacent white pixels (horizontally, vertically, and diagonally) to yellow.

  4. Locate the single blue pixel.

  5. Change the color of the immediately adjacent white pixels (horizontally, vertically, and diagonally) to orange.

  6. The remaining pixels stay the same.

Review Example Phase

example_2

input

[[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 0 0 0 8 0 0]
 [0 0 0 0 0 0 0 0 0]
 [0 0 5 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 0 0 0]]

output

[[0 0 0 0 0 0 8 0 0]
 [0 0 0 0 0 8 8 8 0]
 [0 0 0 0 0 0 8 0 0]
 [0 0 5 0 0 0 0 0 0]
 [0 6 5 6 0 0 0 0 0]
 [0 0 5 0 0 0 0 0 0]
 [0 6 0 6 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]]

images

example_2

input

[[0 0 0 8 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 1 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 1 0 0]
 [0 2 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]]

output

[[0 0 0 8 0 0 0 0 0]
 [0 0 0 0 0 4 0 4 0]
 [0 0 7 0 0 0 2 0 0]
 [0 7 1 7 0 4 0 4 0]
 [0 0 7 0 0 0 0 0 0]
 [0 0 0 0 0 0 7 0 0]
 [4 0 4 0 0 7 1 7 0]
 [0 2 0 0 0 0 7 0 0]
 [4 0 4 0 0 0 0 0 0]]

images

../../../../_images/001-example_2_input15.png ../../../../_images/001-example_2_output15.png

observations

INSTRUCTIONS:

Review Example

pairs of input and output grids will be shown to you one at a time

  • document your initial observations and impressions

    • begin with a verbal description of your perception of the input and output grid

  • use code_execution to examine the grid information and verify the assumptions about size, colors, objects, and transformations. Focus your analysis on aspects like:

    • Counting the occurrences of each color.

    • Identifying the coordinates of pixels that have changed color or position.

    • Determining if the dimensions of the grid have changed.

    • Analyzing the count, size, shape, and relative positions of objects (contiguous blocks of the same color).

  • since the code you use may not be carried forward on following prompts, be sure to have the code print your findings in the output

  • use what you learn to develop a natural language program of the transformation rule.

  • review your findings and try to determine the natural language description of the transformation rule. How does the information captured in the YAML block inform your understanding of the transformation?

use a yaml block to capture details (examples):

input:
  width: X
  height: Y
  colors:
    - N: (count)
  objects:
    - size, position and color - desc

differences:
  cells_changed: N
  colors_changed: desc
  transformation:
    - speculate on transformation rules

final step - provide a thorough natural language program to tell another intelligent entity how to transform the input grid into the output grid

See also