004 • History

puzzle_id:

4-0d3d703e

description:

example_4

timestamp:

24.356.195518

call_count:

4

Begin puzzle: 4-0d3d703e

example_1

input

[[3 1 2]
 [3 1 2]
 [3 1 2]]

output

[[4 5 6]
 [4 5 6]
 [4 5 6]]

images

../../../../_images/000-example_1_input17.png ../../../../_images/000-example_1_output17.png

observations

The user wants me to analyze the first example of an ARC task. I need to describe the input and output grids, use code to analyze them, and then formulate a natural language program that explains the transformation.

Plan:

  1. Describe the input grid.

  2. Describe the output grid.

  3. Use code to analyze the input and output grids (size, colors, differences).

  4. Formulate a natural language program for the transformation.

Okay, let’s analyze the first example.

The input grid is a 3x3 grid. The first column is green, the second column is blue, and the third column is red.

The output grid is also a 3x3 grid. The first column is yellow, the second column is gray, and the third column is magenta.

input:
  width: 3
  height: 3
  colors:
    3: 3 (green)
    1: 3 (blue)
    2: 3 (red)
  objects:
    - size: 3, position: column 1, color: green
    - size: 3, position: column 2, color: blue
    - size: 3, position: column 3, color: red

output:
  width: 3
  height: 3
  colors:
    4: 3 (yellow)
    5: 3 (gray)
    6: 3 (magenta)
  objects:
    - size: 3, position: column 1, color: yellow
    - size: 3, position: column 2, color: gray
    - size: 3, position: column 3, color: magenta

Now let’s use code to identify the differences.

def analyze_grid(grid):
    height = len(grid)
    width = len(grid[0])
    colors = {}
    for row in grid:
        for cell in row:
            colors[cell] = colors.get(cell, 0) + 1
    return {"width": width, "height": height, "colors": colors}

input_grid = [[3, 1, 2], [3, 1, 2], [3, 1, 2]]
output_grid = [[4, 5, 6], [4, 5, 6], [4, 5, 6]]

input_analysis = analyze_grid(input_grid)
output_analysis = analyze_grid(output_grid)

print("Input analysis:", input_analysis)
print("Output analysis:", output_analysis)

differences = {}
if input_analysis['width'] != output_analysis['width'] or input_analysis['height'] != output_analysis['height']:
    differences['size_change'] = 'yes'
else:
    differences['size_change'] = 'no'

changed_cells = 0
color_changes = {}
for r in range(input_analysis['height']):
    for c in range(input_analysis['width']):
        if input_grid[r][c] != output_grid[r][c]:
            changed_cells += 1
            old_color = input_grid[r][c]
            new_color = output_grid[r][c]
            if old_color not in color_changes:
                color_changes[old_color] = new_color

differences['cells_changed'] = changed_cells
differences['color_changes'] = color_changes

print("Differences:", differences)

differences:
  cells_changed: 9
  colors_changed: {3: 4, 1: 5, 2: 6}
  transformation:
    - It looks like each color in the input is consistently mapped to a new color in the output.
    - Green (3) maps to Yellow (4).
    - Blue (1) maps to Gray (5).
    - Red (2) maps to Magenta (6).
    - The grid dimensions remain the same.

Natural language program:

The input grid is a 3x3 grid with three distinct colors arranged in columns: green in the first, blue in the second, and red in the third. The output grid has the same dimensions. To generate the output grid, iterate through each pixel in the input grid. If the pixel is green, change its color to yellow. If the pixel is blue, change its color to gray. If the pixel is red, change its color to magenta. The positions of the colors remain the same; only the colors themselves are changed according to this mapping.

example_2

input

[[2 3 8]
 [2 3 8]
 [2 3 8]]

output

[[6 4 9]
 [6 4 9]
 [6 4 9]]

images

../../../../_images/001-example_2_input17.png ../../../../_images/001-example_2_output17.png

observations

The user wants me to analyze the second example of the ARC task. I need to follow the same steps as before: describe the input and output grids, use code to analyze them, and formulate a natural language program for the transformation.

Plan:

  1. Describe the input grid.

  2. Describe the output grid.

  3. Use code to analyze the input and output grids.

  4. Formulate a natural language program for the transformation.

Okay, let’s analyze the second example.

The input grid is a 3x3 grid. The first column is red, the second column is green, and the third column is azure.

The output grid is also a 3x3 grid. The first column is magenta, the second column is yellow, and the third column is maroon.

input:
  width: 3
  height: 3
  colors:
    2: 3 (red)
    3: 3 (green)
    8: 3 (azure)
  objects:
    - size: 3, position: column 1, color: red
    - size: 3, position: column 2, color: green
    - size: 3, position: column 3, color: azure

output:
  width: 3
  height: 3
  colors:
    6: 3 (magenta)
    4: 3 (yellow)
    9: 3 (maroon)
  objects:
    - size: 3, position: column 1, color: magenta
    - size: 3, position: column 2, color: yellow
    - size: 3, position: column 3, color: maroon

Now let’s use code to identify the differences.

def analyze_grid(grid):
    height = len(grid)
    width = len(grid[0])
    colors = {}
    for row in grid:
        for cell in row:
            colors[cell] = colors.get(cell, 0) + 1
    return {"width": width, "height": height, "colors": colors}

input_grid = [[2, 3, 8], [2, 3, 8], [2, 3, 8]]
output_grid = [[6, 4, 9], [6, 4, 9], [6, 4, 9]]

input_analysis = analyze_grid(input_grid)
output_analysis = analyze_grid(output_grid)

print("Input analysis:", input_analysis)
print("Output analysis:", output_analysis)

differences = {}
if input_analysis['width'] != output_analysis['width'] or input_analysis['height'] != output_analysis['height']:
    differences['size_change'] = 'yes'
else:
    differences['size_change'] = 'no'

changed_cells = 0
color_changes = {}
for r in range(input_analysis['height']):
    for c in range(input_analysis['width']):
        if input_grid[r][c] != output_grid[r][c]:
            changed_cells += 1
            old_color = input_grid[r][c]
            new_color = output_grid[r][c]
            if old_color not in color_changes:
                color_changes[old_color] = new_color

differences['cells_changed'] = changed_cells
differences['color_changes'] = color_changes

print("Differences:", differences)

differences:
  cells_changed: 9
  colors_changed: {2: 6, 3: 4, 8: 9}
  transformation:
    - It appears each color in the input maps consistently to a new color in the output.
    - Red (2) maps to Magenta (6).
    - Green (3) maps to Yellow (4).
    - Azure (8) maps to Maroon (9).
    - The grid dimensions remain the same.

Natural language program:

The input grid is a 3x3 grid with three distinct colors arranged in columns: red in the first, green in the second, and azure in the third. The output grid has the same dimensions. To generate the output grid, iterate through each pixel in the input grid. If the pixel is red, change its color to magenta. If the pixel is green, change its color to yellow. If the pixel is azure, change its color to maroon. The positions of the colors remain the same; only the colors themselves are changed according to this mapping.

example_3

input

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

output

[[1 9 2]
 [1 9 2]
 [1 9 2]]

images

../../../../_images/002-example_3_input12.png ../../../../_images/002-example_3_output12.png

observations

The user wants me to analyze the third example of the ARC task and formulate a natural language program for the transformation. I need to describe the input and output grids, use code to analyze them, and then describe the transformation.

Plan:

  1. Describe the input grid.

  2. Describe the output grid.

  3. Use code to analyze the input and output grids.

  4. Formulate a natural language program for the transformation.

example_3

input

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

output

[[1 9 2]
 [1 9 2]
 [1 9 2]]

images

import matplotlib.pyplot as plt
import numpy as np

def show_grid(grid, title):
    cmap = plt.cm.colors.ListedColormap([(0.93, 0.93, 0.93), (0.12, 0.58, 1.00), (0.86, 0.20, 0.16), (0.31, 0.80, 0.19), (0.90, 0.78, 0.00), (0.33, 0.33, 0.33), (0.90, 0.23, 0.64), (0.90, 0.47, 0.08), (0.53, 0.85, 0.94), (0.57, 0.07, 0.19)])
    bounds = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
    norm = plt.cm.colors.BoundaryNorm(bounds, cmap.N)

    data = np.array(grid)
    fig, ax = plt.subplots()
    ax.imshow(data, cmap=cmap, norm=norm)

    ax.grid(which='major', axis='both', linestyle='-', color='k', linewidth=2)
    ax.set_xticks(np.arange(-.5, len(grid[0])-.5, 1))
    ax.set_yticks(np.arange(-.5, len(grid)-.5, 1))
    ax.set_xticklabels([])
    ax.set_yticklabels([])
    ax.set_title(title)
    for i in range(data.shape[0]):
        for j in range(data.shape[1]):
            ax.text(j, i, str(data[i, j]), ha="center", va="center", color="black")
    plt.show()

input_grid = [[5, 8, 6], [5, 8, 6], [5, 8, 6]]
output_grid = [[1, 9, 2], [1, 9, 2], [1, 9, 2]]

show_grid(input_grid, "Input Grid")
show_grid(output_grid, "Output Grid")

observations

The input grid is a 3x3 grid. The first column is gray, the second column is azure, and the third column is magenta.

The output grid is also a 3x3 grid. The first column is blue, the second column is maroon, and the third column is red.

input:
  width: 3
  height: 3
  colors:
    5: 3 (gray)
    8: 3 (azure)
    6: 3 (magenta)
  objects:
    - size: 3, position: column 1, color: gray
    - size: 3, position: column 2, color: azure
    - size: 3, position: column 3, color: magenta

output:
  width: 3
  height: 3
  colors:
    1: 3 (blue)
    9: 3 (maroon)
    2: 3 (red)
  objects:
    - size: 3, position: column 1, color: blue
    - size: 3, position: column 2, color: maroon
    - size: 3, position: column 3, color: red

def analyze_grid(grid):
    height = len(grid)
    width = len(grid[0])
    colors = {}
    for row in grid:
        for cell in row:
            colors[cell] = colors.get(cell, 0) + 1
    return {"width": width, "height": height, "colors": colors}

input_grid = [[5, 8, 6], [5, 8, 6], [5, 8, 6]]
output_grid = [[1, 9, 2], [1, 9, 2], [1, 9, 2]]

input_analysis = analyze_grid(input_grid)
output_analysis = analyze_grid(output_grid)

print("Input analysis:", input_analysis)
print("Output analysis:", output_analysis)

differences = {}
if input_analysis['width'] != output_analysis['width'] or input_analysis['height'] != output_analysis['height']:
    differences['size_change'] = 'yes'
else:
    differences['size_change'] = 'no'

changed_cells = 0
color_changes = {}
for r in range(input_analysis['height']):
    for c in range(input_analysis['width']):
        if input_grid[r][c] != output_grid[r][c]:
            changed_cells += 1
            old_color = input_grid[r][c]
            new_color = output_grid[r][c]
            if old_color not in color_changes:
                color_changes[old_color] = new_color

differences['cells_changed'] = changed_cells
differences['color_changes'] = color_changes

print("Differences:", differences)

differences:
  cells_changed: 9
  colors_changed: {5: 1, 8: 9, 6: 2}
  transformation:
    - Each color in the input maps consistently to a new color in the output.
    - Gray (5) maps to Blue (1).
    - Azure (8) maps to Maroon (9).
    - Magenta (6) maps to Red (2).
    - The grid dimensions remain the same.

Natural language program:

The input grid is a 3x3 grid with three distinct colors arranged in columns: gray in the first, azure in the second, and magenta in the third. The output grid has the same dimensions. To generate the output grid, iterate through each pixel in the input grid. If the pixel is gray, change its color to blue. If the pixel is azure, change its color to maroon. If the pixel is magenta, change its color to red. The positions of the colors remain the same; only the colors themselves are changed according to this mapping.

example_4

input

[[9 4 2]
 [9 4 2]
 [9 4 2]]

output

[[8 3 6]
 [8 3 6]
 [8 3 6]]

images

../../../../_images/003-example_4_input2.png ../../../../_images/003-example_4_output2.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