004 • Response

puzzle_id:: 5-150deff5
description:: example_summary
timestamp:: 24.329.064813
call_count:: 4
model:: models/gemini-1.5-flash-002

The transformation consistently involves replacing a gray (5) blob with a similar-shaped blob composed of light blue (8) and red (2) pixels. The exact arrangement of the light blue and red pixels within the new blob varies depending on the shape and configuration of the original gray blob. A crucial aspect of the transformation seems to be the consideration of the neighborhood of each gray pixel. Edge and corner pixels appear to be handled differently than interior pixels, suggesting a rule that depends on the number of adjacent gray pixels.

code_execution:

import numpy as np

def analyze_transformation(input_grid, output_grid):
    """Analyzes the transformation from input to output grid."""

    gray_indices = np.where(input_grid == 5)
    gray_pixels = list(zip(*gray_indices))

    red_indices = np.where(output_grid == 2)
    red_pixels = list(zip(*red_indices))

    blue_indices = np.where(output_grid == 8)
    blue_pixels = list(zip(*blue_indices))

    print("Gray Pixel Coordinates:", gray_pixels)
    print("Red Pixel Coordinates:", red_pixels)
    print("Blue Pixel Coordinates:", blue_pixels)


    #Further analysis to identify a correlation between gray pixel neighborhoods and color replacements in output would require a more sophisticated algorithm.  This would involve checking the neighborhood of each gray pixel and correlating that to whether it becomes red or blue in the output.  This requires a more complex algorithm beyond this basic analysis.

    return gray_pixels, red_pixels, blue_pixels

# Example usage (using the first example):
input_grid_ex1 = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
                      [0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0],
                      [0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0],
                      [0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0],
                      [0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0],
                      [0, 0, 0, 5, 0, 0, 5, 5, 0, 0, 0],
                      [0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0],
                      [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
                      [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])

output_grid_ex1 = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
                       [0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0],
                       [0, 0, 8, 8, 2, 2, 2, 0, 0, 0, 0],
                       [0, 0, 0, 2, 8, 8, 0, 0, 0, 0, 0],
                       [0, 0, 0, 2, 8, 8, 8, 8, 0, 0, 0],
                       [0, 0, 0, 2, 0, 0, 8, 8, 0, 0, 0],
                       [0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0],
                       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
                       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])


gray_pixels_ex1, red_pixels_ex1, blue_pixels_ex1 = analyze_transformation(input_grid_ex1, output_grid_ex1)

code_execution_result: 1

Gray Pixel Coordinates: [(np.int64(1), np.int64(2)), (np.int64(1), np.int64(3)), (np.int64(2), np.int64(2)), (np.int64(2), np.int64(3)), (np.int64(2), np.int64(4)), (np.int64(2), np.int64(5)), (np.int64(2), np.int64(6)), (np.int64(3), np.int64(3)), (np.int64(3), np.int64(4)), (np.int64(3), np.int64(5)), (np.int64(4), np.int64(3)), (np.int64(4), np.int64(4)), (np.int64(4), np.int64(5)), (np.int64(4), np.int64(6)), (np.int64(4), np.int64(7)), (np.int64(5), np.int64(3)), (np.int64(5), np.int64(6)), (np.int64(5), np.int64(7)), (np.int64(6), np.int64(5)), (np.int64(6), np.int64(6)), (np.int64(6), np.int64(7))]
Red Pixel Coordinates: [(np.int64(2), np.int64(4)), (np.int64(2), np.int64(5)), (np.int64(2), np.int64(6)), (np.int64(3), np.int64(3)), (np.int64(4), np.int64(3)), (np.int64(5), np.int64(3)), (np.int64(6), np.int64(5)), (np.int64(6), np.int64(6)), (np.int64(6), np.int64(7))]
Blue Pixel Coordinates: [(np.int64(1), np.int64(2)), (np.int64(1), np.int64(3)), (np.int64(2), np.int64(2)), (np.int64(2), np.int64(3)), (np.int64(3), np.int64(4)), (np.int64(3), np.int64(5)), (np.int64(4), np.int64(4)), (np.int64(4), np.int64(5)), (np.int64(4), np.int64(6)), (np.int64(4), np.int64(7)), (np.int64(5), np.int64(6)), (np.int64(5), np.int64(7))]

The code provides coordinate information for gray, red, and blue pixels. A more sophisticated algorithm would be needed to analyze the neighborhood of each gray pixel and establish the rule determining whether a pixel becomes red or blue. The current tool output provides a foundation for that more complex analysis. The next step would be to write an algorithm that analyzes the number of gray neighbors for each original gray pixel and attempts to correlate that to whether it transformed into red or blue. This would require iterative development and testing against the provided examples.

time
response time	total elapsed
8.797	83.221

usage
token type	call count	total used
Prompt	10927	24624
Response	1880	8645
Total	12807	33269
Cached	0	0