002 • History

puzzle_id:

1-3aa6fb7a

description:

example_2

timestamp:

24.357.081407

call_count:

2

Begin puzzle: 1-3aa6fb7a

example_1

input

[[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

[[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]]

images

../../../../_images/000-example_1_input20.png ../../../../_images/000-example_1_output20.png

observations

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:

  1. Perceptual Description: Describe the input and output grids verbally.

  2. Code Examination: Use code to extract grid information (dimensions, colors, object properties, differences).

  3. YAML Documentation: Capture key information about the input and differences in YAML format.

  4. Transformation Rule (Hypothesis): Based on the observations, propose a preliminary natural language description of the transformation.

  5. 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).

example_2

input

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

output

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

images

../../../../_images/001-example_2_input20.png ../../../../_images/001-example_2_output20.png

observations

INSTRUCTIONS:

above is a pair of example input and output grids

  • 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.

    • How to identify 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

You will examine and analyze the example grids

For each example pair, your goal is to derive a natural language description of the transformation rule that explains how the input is changed to produce the output. This “natural language program” should describe the steps or logic involved in the transformation.

the natural language program should be sufficient for an intelligent agent to perform the operation of generating an output grid from the input, without the benefit of seeing the examples. So be sure that the provide

  • context for understanding the input grid (objects, organization and important colors) particularly context for how to identify the ‘objects’

  • process for initializing the output grid (copy from input or set size and fill)

  • describe the color palette to be used in the output

  • describe how to determine which pixels should change in the output

For example, it might state:

  • copy input to working output

  • identify sets of pixels in blue (1) rectangles in working grid

  • identify to largest rectangle

  • set the largest rectangle’s pixels to red (2)

But remember - any information that describe the story of the transformations is desired. Be flexible and creative.

See also