004 • Response
- puzzle_id:
2-0ca9ddb6
- description:
example_summary
- timestamp:
24.356.195518
- call_count:
4
- model:
gemini-2.0-flash-thinking-exp-1219
The user wants me to analyze the provided example and compare it with the previous examples to refine the transformation rule.
Comparing with previous examples:
In the first puzzle (2-0ca9ddb6), all non-white single pixels caused adjacent white pixels to change color (Red -> Yellow, Blue -> Orange, Gray -> Magenta, Azure -> Azure).
In the current puzzle, only red and blue pixels cause adjacent white pixels to change color. Magenta does not have this effect.
This suggests the transformation rule is based on the specific color of the non-white pixel.
Revised Transformation Hypothesis:
The transformation involves identifying non-white pixels of specific colors (red and blue) and changing their adjacent white pixels to a corresponding color.
Let’s verify this with the provided example. The red pixel at (2, 2) has adjacent white pixels changed to yellow. The blue pixel at (7, 3) has adjacent white pixels changed to orange. The magenta pixel at (5, 6) does not cause any change in its adjacent white pixels.
import numpy as np
example_input = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 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, 0, 0, 0, 0, 0, 6, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0]])
example_output = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 4, 0, 4, 0, 0, 0, 0, 0],
[0, 0, 2, 0, 0, 0, 0, 0, 0],
[0, 4, 0, 4, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 6, 0, 0],
[0, 0, 0, 7, 0, 0, 0, 0, 0],
[0, 0, 7, 1, 7, 0, 0, 0, 0],
[0, 0, 0, 7, 0, 0, 0, 0, 0]])
diff = example_input != example_output
diff_coords = np.where(diff)
print("Coordinates of differences:", list(zip(diff_coords[0], diff_coords[1])))
input_red_coords = np.where(example_input == 2)
print("Red pixel coordinates in input:", list(zip(input_red_coords[0], input_red_coords[1])))
input_blue_coords = np.where(example_input == 1)
print("Blue pixel coordinates in input:", list(zip(input_blue_coords[0], input_blue_coords[1])))
input_magenta_coords = np.where(example_input == 6)
print("Magenta pixel coordinates in input:", list(zip(input_magenta_coords[0], input_magenta_coords[1])))
Summary of Observations:
The transformation rule focuses on specific colors present in the input grid.
Red pixels: For each red pixel in the input grid, the immediately adjacent white pixels in the output grid become yellow.
Blue pixels: For each blue pixel in the input grid, the immediately adjacent white pixels in the output grid become orange.
Magenta pixels: Magenta pixels do not cause any changes to the color of adjacent white pixels.
Natural Language Program:
The transformation takes an input grid and generates an output grid by changing the color of white pixels adjacent to specific colored pixels.
To create the output grid:
Initialize the output grid by making a copy of the input grid.
Iterate through each cell of the input grid.
- If a cell in the input grid is red (2):
Identify all the immediately adjacent cells (horizontally, vertically, and diagonally) in the output grid.
If an adjacent cell in the output grid is white (0), change its color to yellow (4).
- If a cell in the input grid is blue (1):
Identify all the immediately adjacent cells (horizontally, vertically, and diagonally) in the output grid.
If an adjacent cell in the output grid is white (0), change its color to orange (7).
Pixels of other colors (e.g., magenta) in the input grid do not cause any changes to the color of adjacent white pixels in the output grid.
The original non-white pixels remain unchanged.
Ruminate Phase
Review All Examples and Findings
Across the provided examples, a consistent pattern emerges regarding the transformation from the input grid to the output grid. The transformation is localized around specific colored pixels in the input and affects the color of their adjacent white pixels in the output.
Red pixels (2) in the input: Cause adjacent white pixels (0) in the output to become yellow (4).
Blue pixels (1) in the input: Cause adjacent white pixels (0) in the output to become orange (7).
Magenta pixels (6) in the input: Do not cause any change to adjacent white pixels in the output.
It’s important to note that the transformation only affects white pixels that are immediately adjacent (horizontally, vertically, or diagonally) to the red or blue pixels. The original red, blue, and magenta pixels themselves remain unchanged in the output grid.
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):
pixel_color = input_grid[r, c]
if pixel_color == 2: # Red
for dr in [-1, 0, 1]:
for dc in [-1, 0, 1]:
if dr == 0 and dc == 0:
continue
nr, nc = r + dr, c + dc
if 0 <= nr < rows and 0 <= nc < cols and output_grid[nr, nc] == 0:
output_grid[nr, nc] = 4
elif pixel_color == 1: # Blue
for dr in [-1, 0, 1]:
for dc in [-1, 0, 1]:
if dr == 0 and dc == 0:
continue
nr, nc = r + dr, c + dc
if 0 <= nr < rows and 0 <= nc < cols and output_grid[nr, nc] == 0:
output_grid[nr, nc] = 7
return output_grid
# Example 1
input_ex1 = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 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, 0, 0, 0, 0, 0, 6, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0]])
output_ex1 = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 4, 0, 4, 0, 0, 0, 0, 0],
[0, 0, 2, 0, 0, 0, 0, 0, 0],
[0, 4, 0, 4, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 6, 0, 0],
[0, 0, 0, 7, 0, 0, 0, 0, 0],
[0, 0, 7, 1, 7, 0, 0, 0, 0],
[0, 0, 0, 7, 0, 0, 0, 0, 0]])
print("Example 1 matches:", np.array_equal(apply_transformation(input_ex1), output_ex1))
Final Natural Language Program:
The transformation process takes an input grid and generates an output grid based on the colors of specific pixels in the input.
To produce the output grid:
Start by creating a copy of the input grid as the initial output grid.
Examine each pixel in the input grid.
- If a pixel in the input grid is red (color value 2):
Identify all the immediately adjacent pixels (horizontally, vertically, and diagonally) in the output grid.
For each adjacent pixel in the output grid, if its current color is white (color value 0), change its color to yellow (color value 4).
- If a pixel in the input grid is blue (color value 1):
Identify all the immediately adjacent pixels (horizontally, vertically, and diagonally) in the output grid.
For each adjacent pixel in the output grid, if its current color is white (color value 0), change its color to orange (color value 7).
Pixels of other colors in the input grid (such as magenta with color value 6) do not trigger any changes in the adjacent white pixels of the output grid.
The original positions and colors of the red, blue, and magenta pixels from the input grid are preserved in the output grid.
response time |
total elapsed |
|---|---|
20.485 |
89.114 |
token type |
call count |
total used |
|---|---|---|
Prompt |
13283 |
33378 |
Response |
2642 |
11492 |
Total |
15925 |
44870 |
Cached |
0 |
0 |
See also