003 • Response

puzzle_id:: 3-1e0a9b12
description:: example_3
timestamp:: 24.356.195518
call_count:: 3
model:: gemini-2.0-flash-thinking-exp-1219

The user wants me to analyze the third example of the ARC task and describe the transformation.

Plan:

Describe the input and output grids.
Use code to analyze the grids and identify differences.
Formulate a natural language program.
Create YAML blocks to summarize the input and the differences between input and output.

Input Grid Analysis:

The input grid is a 5x5 grid. It contains blue (1), green (3), red (2), and magenta (6) pixels on a white (0) background. There’s a vertical line of green pixels in the second column. There are blue pixels in the first and fourth rows. There’s a red pixel in the third row. There’s a magenta pixel in the fourth row.

Output Grid Analysis:

The output grid is also a 5x5 grid. The top two rows are all white. The green pixels are now concentrated in the third and fourth rows. The blue pixels are also in the third and fourth rows. The red and magenta pixels are in the last row.

Identifying Transformations:

It appears the colored pixels are moving downwards. The green pixels are moving down, maintaining their column. The blue pixels are also moving down. The red and magenta pixels are moving to the last row.

import numpy as np

input_grid = np.array([[0, 0, 0, 1, 0],
                       [0, 3, 0, 0, 0],
                       [0, 3, 0, 1, 2],
                       [6, 0, 0, 0, 0],
                       [0, 3, 0, 0, 0]])

output_grid = np.array([[0, 0, 0, 0, 0],
                        [0, 0, 0, 0, 0],
                        [0, 3, 0, 0, 0],
                        [0, 3, 0, 1, 0],
                        [6, 3, 0, 1, 2]])

input_colors, input_counts = np.unique(input_grid, return_counts=True)
output_colors, output_counts = np.unique(output_grid, return_counts=True)

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

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

input_color_coords = {}
for color in np.unique(input_grid):
    coords = np.where(input_grid == color)
    input_color_coords[color] = list(zip(coords[0], coords[1]))
print("Input color coordinates:", input_color_coords)

output_color_coords = {}
for color in np.unique(output_grid):
    coords = np.where(output_grid == color)
    output_color_coords[color] = list(zip(coords[0], coords[1]))
print("Output color coordinates:", output_color_coords)

input:
  width: 5
  height: 5
  colors:
    0: 18
    1: 2
    3: 3
    2: 1
    6: 1
  objects:
    - size: 2, positions: [(0, 3), (2, 3)], color: blue
    - size: 3, positions: [(1, 1), (2, 1), (4, 1)], color: green
    - size: 1, position: (2, 4), color: red
    - size: 1, position: (3, 0), color: magenta

differences:
  cells_changed: 10
  colors_changed:
    - from blue at (0, 3) to white at (0, 3)
    - from green at (1, 1) to white at (1, 1)
    - from blue at (2, 3) to white at (2, 3)
    - from red at (2, 4) to white at (2, 4)
    - from magenta at (3, 0) to white at (3, 0)
    - from green at (4, 1) to white at (4, 1)
    - from white at (2, 1) to green at (2, 1)
    - from white at (3, 1) to green at (3, 1)
    - from white at (3, 3) to blue at (3, 3)
    - from white at (4, 0) to magenta at (4, 0)
    - from white at (4, 3) to blue at (4, 3)
    - from white at (4, 4) to red at (4, 4)

  transformation:
    - Blue pixels move down.
    - Green pixels move down.
    - Red pixel moves to the last row.
    - Magenta pixel moves to the last row.

Natural Language Program:

Create an output grid with the same dimensions as the input grid, initialized with white pixels.
Identify all green pixels in the input grid. For each green pixel, place a green pixel in the output grid, shifted down by two rows, maintaining the original column index.
Identify all blue pixels in the input grid. For each blue pixel, place a blue pixel in the output grid, shifted down by three rows, maintaining the original column index.
Identify the red pixel in the input grid. Place the red pixel in the last row of the output grid, in the same column.
Identify the magenta pixel in the input grid. Place the magenta pixel in the first column of the last row of the output grid.

Revised Natural Language Program:

Create an output grid with the same dimensions as the input grid, initialized with white pixels.
Move all green pixels downwards by two rows, maintaining their column.
Move all blue pixels downwards by three rows, maintaining their column.
Move the red pixel to the last row, keeping its column.
Move the magenta pixel to the first column of the last row.

Consider the case where the downward shift goes beyond the grid boundaries.

Revised Natural Language Program:

Create an output grid with the same dimensions as the input grid, initialized with white pixels.
For each green pixel at (r, c) in the input grid, place a green pixel at (r+2, c) in the output grid, provided r+2 is within the grid boundaries.
For each blue pixel at (r, c) in the input grid, place a blue pixel at (r+3, c) in the output grid, provided r+3 is within the grid boundaries.
For the red pixel at (r, c) in the input grid, place a red pixel at (height-1, c) in the output grid.
For the magenta pixel at (r, c) in the input grid, place a magenta pixel at (height-1, 0) in the output grid.

input:
  width: 5
  height: 5
  colors:
    0: 18
    1: 2
    3: 3
    2: 1
    6: 1
  objects:
    - size: 2, positions: [(0, 3), (2, 3)], color: blue
    - size: 3, positions: [(1, 1), (2, 1), (4, 1)], color: green
    - size: 1, position: (2, 4), color: red
    - size: 1, position: (3, 0), color: magenta

differences:
  cells_changed: 10
  colors_changed:
    - from blue at (0, 3) to white at (0, 3)
    - from green at (1, 1) to white at (1, 1)
    - from blue at (2, 3) to white at (2, 3)
    - from red at (2, 4) to white at (2, 4)
    - from magenta at (3, 0) to white at (3, 0)
    - from green at (4, 1) to white at (4, 1)
    - from white at (2, 1) to green at (2, 1)
    - from white at (3, 1) to green at (3, 1)
    - from white at (3, 3) to blue at (3, 3)
    - from white at (4, 0) to magenta at (4, 0)
    - from white at (4, 3) to blue at (4, 3)
    - from white at (4, 4) to red at (4, 4)

  transformation:
    - Blue pixels move down by three rows.
    - Green pixels move down by two rows.
    - The red pixel moves to the last row, maintaining its column.
    - The magenta pixel moves to the first column of the last row.

Natural Language Program:

Create an output grid with the same dimensions as the input grid, initialized with white pixels.
For each green pixel at row r and column c in the input grid, place a green pixel at row r + 2 and column c in the output grid.
For each blue pixel at row r and column c in the input grid, place a blue pixel at row r + 3 and column c in the output grid.
For the red pixel at row r and column c in the input grid, place a red pixel at the last row and column c in the output grid.
For the magenta pixel at row r and column c in the input grid, place a magenta pixel at the last row and the first column in the output grid.

time
response time	total elapsed
18.52	67.251

usage
token type	call count	total used
Prompt	10195	21015
Response	2386	8649
Total	12581	29664
Cached	0	0