004 • Response

puzzle_id:: 1-3aa6fb7a
description:: test input
timestamp:: 24.356.195518
call_count:: 4
model:: gemini-2.0-flash-thinking-exp-1219

The user has provided a test input grid for the ARC task 1-3aa6fb7a. I need to apply the derived natural language program to predict the output grid.

Natural Language Program:

Context: The input is a grid containing white (0) and azure (8) pixels. Identify the connected regions of azure pixels, which form ‘L’ shapes.
Initialization: Create a copy of the input grid to serve as the initial state of the output grid.
Color Palette: The output grid will consist of white (0), azure (8), and blue (1) pixels.
Transformation:
- Iterate through each pixel in the input grid.
- If a pixel is white (0), examine its immediate orthogonal neighbors (up, down, left, right).
- Count the number of orthogonal neighbors that are azure (8).
- If exactly two orthogonal neighbors are azure, check if these two azure neighbors are also orthogonally adjacent to each other.
- If both conditions are met, change the color of the white pixel in the output grid to blue (1).

Applying the transformation to the test input:

Input grid:

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

Iterate through white pixels and check the conditions:

(0, 0): Neighbors: (0, 1)W, (1, 0)Az. Count Azure = 1.
(0, 1): Neighbors: (0, 0)W, (0, 2)W, (1, 1)Az. Count Azure = 1.
(0, 2): Neighbors: (0, 1)W, (0, 3)W. Count Azure = 0.
(0, 3): Neighbors: (0, 2)W, (0, 4)W. Count Azure = 0.
(0, 4): Neighbors: (0, 3)W, (0, 5)Az. Count Azure = 1.
(1, 2): Neighbors: (0, 2)W, (2, 2)W, (1, 1)Az. Count Azure = 1.
(1, 3): Neighbors: (1, 2)W, (1, 4)W. Count Azure = 0.
(1, 4): Neighbors: (1, 3)W, (1, 5)W. Count Azure = 0.
(2, 1): Neighbors: (1, 1)Az, (3, 1)W, (2, 0)Az. Azure neighbors: (1,1), (2,0). They are adjacent. Change (2,1) to blue.
(2, 2): Neighbors: (1, 2)W, (3, 2)W, (2, 1)W. Count Azure = 0.
(2, 3): Neighbors: (2, 2)W, (2, 4)W. Count Azure = 0.
(2, 4): Neighbors: (2, 3)W, (2, 5)W. Count Azure = 0.
(2, 5): Neighbors: (1, 5)Az, (3, 5)W. Count Azure = 1.
(2, 6): Neighbors: (1, 6)Az. Count Azure = 1.
(3, 0): Neighbors: (2, 0)Az, (4, 0)W. Count Azure = 1.
(3, 1): Neighbors: (2, 1)W, (4, 1)W. Count Azure = 0.
(3, 2): Neighbors: (3, 1)W, (3, 3)Az. Count Azure = 1.
(3, 5): Neighbors: (2, 5)W, (4, 5)Az. Count Azure = 1.
(3, 6): Neighbors: (0, 6)Az, (4, 6)W. Count Azure = 1.
(4, 0): Neighbors: (3, 0)W, (5, 0)W. Count Azure = 0.
(4, 1): Neighbors: (5, 1)Az. Count Azure = 1.
(4, 6): Neighbors: (3, 6)W. Count Azure = 0.
(5, 2): Neighbors: (4, 2)Az, (6, 2)W, (5, 1)Az. Azure neighbors: (4,2), (5,1). They are adjacent. Change (5,2) to blue.
(5, 3): Neighbors: (5, 2)W. Count Azure = 0.
(5, 4): Neighbors: Count Azure = 0.
(5, 5): Neighbors: Count Azure = 0.
(5, 6): Neighbors: Count Azure = 0.
(6, 2): Neighbors: (5, 2)W. Count Azure = 0.
(6, 3): Neighbors: Count Azure = 0.
(6, 4): Neighbors: Count Azure = 0.
(6, 5): Neighbors: Count Azure = 0.
(6, 6): Neighbors: Count Azure = 0.

Predicted output:

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

import numpy as np

def apply_transformation(input_grid):
    output_grid = np.copy(input_grid)
    rows, cols = input_grid.shape
    for r in range(rows):
        for c in range(cols):
            if input_grid[r, c] == 0:
                azure_neighbors = []
                for dr, dc in [(0, 1), (0, -1), (1, 0), (-1, 0)]:
                    nr, nc = r + dr, c + dc
                    if 0 <= nr < rows and 0 <= nc < cols and input_grid[nr, nc] == 8:
                        azure_neighbors.append((nr, nc))

                if len(azure_neighbors) == 2:
                    r1, c1 = azure_neighbors[0]
                    r2, c2 = azure_neighbors[1]
                    if abs(r1 - r2) + abs(c1 - c2) == 1:
                        output_grid[r, c] = 1
    return output_grid

test_input = np.array([[0, 0, 0, 0, 0, 8, 8],
                       [8, 8, 0, 0, 0, 0, 8],
                       [8, 0, 0, 0, 0, 0, 0],
                       [0, 0, 0, 8, 0, 0, 0],
                       [0, 0, 0, 8, 8, 0, 0],
                       [0, 8, 0, 0, 0, 0, 0],
                       [8, 8, 0, 0, 0, 0, 0]])

predicted_output = apply_transformation(test_input)
print(predicted_output)

time
response time	total elapsed
16.81	67.795

usage
token type	call count	total used
Prompt	10234	26132
Response	2161	8774
Total	12395	34906
Cached	0	0