gpt4

---

I'm doing Prolog experiments.


The x and y coordinates represent a 0-indexed grid.


```prolog
% Example 0 input grid 9cols_9rows
object(input0_color4_x1_y2_width4_height3_mass8_shapePlus_scaleUnknown, transform(all)).

% Example 0 output grid 8cols_6rows
object(output0_color4_x0_y0_width8_height6_mass32_shapePlus_scaleUnknown, transform(all)).

% Example 1 input grid 9cols_9rows
object(input1_color4_x3_y1_width3_height3_mass4_shapeLWith45DegreeLine_scalex1_scaley1, transform(rot90_flip)).

% Example 1 output grid 6cols_6rows
object(output1_color4_x0_y0_width6_height6_mass16_shapeLWith45DegreeLine_scalex2_scaley2, transform(rot90_flip)).

% Example 2 input grid 9cols_9rows
object(input2_color4_x1_y4_width3_height4_mass6_shapeUnclassified_scalex1_scaley1, transform(rot90)).

% Example 2 output grid 6cols_8rows
object(output2_color4_x0_y0_width6_height8_mass24_shapeUnclassified_scalex2_scaley2, transform(rot90)).
```


Think step by step, what are the transformations across all the examples, that goes from the input to the output.
With the following example, I want you to predict what the output should be


```prolog

% Example 3 input grid 9cols_9rows
object(input3_color4_x3_y1_width5_height3_mass7_shapeUnclassified_scalex1_scaley1, transform(rot0_rot180_flip_flip180)).

% Example 3 output grid 10cols_6rows
PREDICT the lines that starts with object(output3_
```
Repeat the previous example prolog code, with the PREDICT replaced with your predictions.

---

Based on the first three examples, it appears that the transformations that are applied to go from the input to the output include:

1. The x and y coordinates both change to (0,0) in the output.
2. The width and height both seem to scale up, potentially in proportion to the mass. If the mass is multiplied by a factor, the width and height appear to be multiplied by the same factor.
3. The mass appears to multiply by a factor of 4.
4. The shape remains the same.
5. The scaling seems to multiply by a factor of 2 on both x and y axes.
6. The transformations applied to the object remain the same.

Using these observations, we can try to predict the output for the given input. Here is the input:

```prolog
% Example 3 input grid 9cols_9rows
object(input3_color4_x3_y1_width5_height3_mass7_shapeUnclassified_scalex1_scaley1, transform(rot0_rot180_flip_flip180)).
```

We would then predict the following output:

```prolog
% Example 3 output grid 10cols_6rows
object(output3_color4_x0_y0_width10_height6_mass28_shapeUnclassified_scalex2_scaley2, transform(rot0_rot180_flip_flip180)).
```

This prediction assumes that the width scales up from 5 to 10 and the height from 3 to 6 (i.e., in proportion to their original sizes), and that the mass scales up from 7 to 28 (i.e., multiplying by 4). The x and y coordinates have both changed to (0,0), the shape remains 'Unclassified', the scale is multiplied by 2 on both x and y axes, and the transformations remain the same as in the input.

---

Nit pick: The outputted prolog should be 1 code piece
