002 • History
- puzzle_id:
1-3aa6fb7a
- description:
example_2
- timestamp:
24.356.195518
- 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
observations
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
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
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_executionto 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