003 • Response
- puzzle_id:
5-150deff5
- description:
example_3
- timestamp:
24.329.064813
- call_count:
3
- model:
models/gemini-1.5-flash-002
Review Examples Phase
Example 1:
The input grid contains a blob of gray (5) pixels. The output grid retains the same blob shape, but the gray pixels are replaced with a pattern of light blue (8) and red (2) pixels. The pattern seems to be based on the position of the gray pixel within the blob, likely considering neighboring pixels.
code_execution:
import numpy as np
input_grid = 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 = 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_indices = np.where(input_grid == 5)
print(f"Gray pixel coordinates: {gray_indices}")
# Count occurrences of 2 and 8 in the output
count_2 = np.count_nonzero(output_grid == 2)
count_8 = np.count_nonzero(output_grid == 8)
print(f"Number of 2s: {count_2}")
print(f"Number of 8s: {count_8}")
code_execution_result: 1
Gray pixel coordinates: (array([1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6]), array([2, 3, 2, 3, 4, 5, 6, 3, 4, 5, 3, 4, 5, 6, 7, 3, 6, 7, 5, 6, 7]))
Number of 2s: 9
Number of 8s: 12
input:
width: 11
height: 9
colors:
- 0: 91
- 5: 21
objects:
- size: 21, position: centered, color: gray
output:
width: 11
height: 9
colors:
- 0: 91
- 2: 10
- 8: 11
objects:
- size: 21, position: centered, color: a mix of light blue (8) and red (2) pixels. Shape is maintained.
differences:
cells_changed: 21
colors_changed: Gray (5) pixels replaced by light blue (8) and red (2) pixels.
transformation:
- A gray blob is transformed. Gray pixels are replaced with light blue and red pixels in a pattern that appears to depend on the local neighborhood of each gray pixel. The overall shape is preserved.
Example 2:
The input shows a heart-shaped configuration of gray (5) pixels. The output maintains the heart shape but replaces gray pixels with a pattern of light blue (8) and red (2). The replacement pattern seems to be based on position within the heart shape.
code_execution:
import numpy as np
input_grid = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 5, 5, 5, 5, 5, 5, 0, 0, 0],
[0, 5, 5, 5, 5, 5, 5, 0, 0, 0],
[0, 0, 0, 5, 0, 0, 5, 0, 0, 0],
[0, 0, 0, 0, 5, 5, 5, 0, 0, 0],
[0, 0, 0, 0, 5, 5, 5, 0, 0, 0],
[0, 0, 0, 0, 5, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
output_grid = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 8, 8, 2, 8, 8, 2, 0, 0, 0],
[0, 8, 8, 2, 8, 8, 2, 0, 0, 0],
[0, 0, 0, 2, 0, 0, 2, 0, 0, 0],
[0, 0, 0, 0, 2, 8, 8, 0, 0, 0],
[0, 0, 0, 0, 2, 8, 8, 0, 0, 0],
[0, 0, 0, 0, 2, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
gray_indices = np.where(input_grid == 5)
print(f"Gray pixel coordinates: {gray_indices}")
# Count occurrences of 2 and 8 in the output
count_2 = np.count_nonzero(output_grid == 2)
count_8 = np.count_nonzero(output_grid == 8)
print(f"Number of 2s: {count_2}")
print(f"Number of 8s: {count_8}")
code_execution_result: 1
Gray pixel coordinates: (array([1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6]), array([1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 3, 6, 4, 5, 6, 4, 5, 6, 4]))
Number of 2s: 9
Number of 8s: 12
input:
width: 10
height: 8
colors:
- 0: 63
- 5: 17
objects:
- size: 17, position: heart shape, color: gray
output:
width: 10
height: 8
colors:
- 0: 63
- 2: 8
- 8: 9
objects:
- size: 17, position: heart shape, color: a mix of light blue (8) and red (2) pixels. Shape is maintained.
differences:
cells_changed: 17
colors_changed: Gray (5) pixels are replaced with a pattern of light blue (8) and red (2) pixels.
transformation:
- A gray heart shape is transformed. Gray pixels are replaced by light blue and red pixels in a pattern that seems to depend on the position within the heart shape. The overall shape is preserved.
Example 3:
The input grid has a gray (5) shape that resembles an incomplete rectangle. The output grid maintains the same shape but replaces the gray pixels with a pattern of light blue (8) and red (2) pixels. The replacement pattern appears consistent, but a rule is not yet apparent.
code_execution:
import numpy as np
input_grid = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 5, 5, 5, 5, 5, 0, 0, 0],
[0, 0, 0, 0, 5, 5, 0, 0, 0],
[0, 0, 0, 5, 0, 0, 0, 0, 0],
[0, 0, 0, 5, 5, 5, 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]])
output_grid = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 2, 2, 2, 8, 8, 0, 0, 0],
[0, 0, 0, 0, 8, 8, 0, 0, 0],
[0, 0, 0, 2, 0, 0, 0, 0, 0],
[0, 0, 0, 2, 8, 8, 0, 0, 0],
[0, 0, 0, 2, 8, 8, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0]])
gray_indices = np.where(input_grid == 5)
print(f"Gray pixel coordinates: {gray_indices}")
# Count occurrences of 2 and 8 in the output
count_2 = np.count_nonzero(output_grid == 2)
count_8 = np.count_nonzero(output_grid == 8)
print(f"Number of 2s: {count_2}")
print(f"Number of 8s: {count_8}")
code_execution_result: 1
Gray pixel coordinates: (array([1, 1, 1, 1, 1, 2, 2, 3, 4, 4, 4, 5, 5, 5]), array([1, 2, 3, 4, 5, 4, 5, 3, 3, 4, 5, 3, 4, 5]))
Number of 2s: 6
Number of 8s: 8
input:
width: 9
height: 8
colors:
- 0: 64
- 5: 14
objects:
- size: 14, position: resembles an incomplete rectangle, color: gray
output:
width: 9
height: 8
colors:
- 0: 64
- 2: 6
- 8: 8
objects:
- size: 14, position: resembles an incomplete rectangle, color: a mix of light blue (8) and red (2) pixels. Shape is maintained.
differences:
cells_changed: 14
colors_changed: Gray (5) pixels are replaced by light blue (8) and red (2) pixels.
transformation:
- A gray, incomplete rectangular shape is transformed. Gray pixels are replaced with light blue and red pixels in a pattern that seems consistent but the exact rule is still unclear. The overall shape is preserved.
Ruminate Phase:
From the three examples, we observe a consistent pattern: A shape composed of gray (5) pixels in the input grid is transformed into a similar shape in the output grid. The gray pixels are replaced by a combination of light blue (8) and red (2) pixels. The exact replacement pattern seems to depend on the local neighborhood of each gray pixel and potentially its position within the overall shape. The examples suggest that edge pixels and corner pixels of the gray shapes are treated differently than interior pixels. More examples are needed to definitively determine the rule governing the replacement. However, based on these three, I hypothesize a rule involving simple adjacency checks (checking for neighbors of value 5) to determine whether a pixel becomes red or light blue.
Natural Language Program (Hypothetical):
Identify Gray Blob: Locate all connected components of gray (5) pixels in the input grid.
Iterate Through Gray Pixels: For each gray pixel:
Check Neighbors: Determine the number of neighboring pixels (horizontally and vertically adjacent) that are also gray (5).
Apply Replacement Rule:
If the number of gray neighbors is 0, 1, or 2, replace the pixel with red (2).
If the number of gray neighbors is 3 or more, replace the pixel with light blue (8).
Output Grid: The resulting grid with the modified pixels is the output.
Code Execution (Validation):
This code requires more sophisticated logic to fully implement the described neighborhood analysis. The following is a starting point to illustrate an approach to analyzing neighborhoods, but does not cover the full complexity required for all examples.
code_execution:
import numpy as np
def transform_grid(grid):
#Simplified neighborhood check; needs refinement for full accuracy.
new_grid = np.copy(grid)
gray_indices = np.where(grid == 5)
for i, j in zip(*gray_indices):
count = 0
for x,y in [(i-1,j),(i+1,j),(i,j-1),(i,j+1)]:
if 0<=x<grid.shape[0] and 0<=y<grid.shape[1] and grid[x,y]==5:
count+=1
if count <=2:
new_grid[i, j] = 2
else:
new_grid[i, j] = 8
return new_grid
# Test with Example 1
input_grid = 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 = transform_grid(input_grid)
print(output_grid)
code_execution_result: 1
[[0 0 0 0 0 0 0 0 0 0 0]
[0 0 2 2 0 0 0 0 0 0 0]
[0 0 2 8 8 8 2 0 0 0 0]
[0 0 0 8 8 8 0 0 0 0 0]
[0 0 0 8 8 8 8 2 0 0 0]
[0 0 0 2 0 0 8 8 0 0 0]
[0 0 0 0 0 2 8 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]]
The code execution shows that a simplified neighborhood check partially works. The output is not pixel-perfect compared to the example outputs, but the general pattern is being captured. To make this more accurate, the code would need refinements to handle edge cases and more complex neighbor relationships. Additional examples would be particularly helpful to refine the neighbor analysis and determine more precisely how the replacement rule operates for different configurations of gray pixels. Further development of the rule is needed to correctly handle all the different configurations observed in the examples. The current attempt provides a reasonable starting point but is not fully accurate without further data and refinement.
response time |
total elapsed |
|---|---|
56.596 |
74.313 |
token type |
call count |
total used |
|---|---|---|
Prompt |
6534 |
13697 |
Response |
4559 |
6765 |
Total |
11093 |
20462 |
Cached |
0 |
0 |
See also