gpt4

---

I'm doing Prolog experiments.


The grid is 1-indexed and does allow negative indices.


Top-Left Bottom-Right (TLBR) is used for object bounding boxes, like tY_lX_bY_rX where t=top l=left b=bottom r=right.


The width of the object bounding box has a 'w' prefix, like 'w5' is width=5.
The height of the object bounding box has a 'h' prefix, like 'h3' is height=3.


```prolog
% Example 1 input grid_width12_height17
object(input1_color8_t1_l10_b1_r10_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input1_color8_t1_l8_b1_r8_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input1_color8_t1_l6_b1_r6_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input1_color8_t1_l2_b1_r2_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input1_color2_t11_l1_b11_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input1_color2_t5_l1_b5_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).

% Example 1 output grid_width12_height17
object(output1_color8_t11_l12_b17_r12_w1_h7_mass7_shapeRectangle_scalex1_scaley7, transform(all)).
object(output1_color8_t11_l10_b17_r10_w1_h7_mass7_shapeRectangle_scalex1_scaley7, transform(all)).
object(output1_color8_t11_l8_b17_r8_w1_h7_mass7_shapeRectangle_scalex1_scaley7, transform(all)).
object(output1_color8_t11_l4_b17_r4_w1_h7_mass7_shapeRectangle_scalex1_scaley7, transform(all)).
object(output1_color8_t5_l11_b10_r11_w1_h6_mass6_shapeRectangle_scalex1_scaley6, transform(all)).
object(output1_color8_t5_l9_b10_r9_w1_h6_mass6_shapeRectangle_scalex1_scaley6, transform(all)).
object(output1_color8_t5_l7_b10_r7_w1_h6_mass6_shapeRectangle_scalex1_scaley6, transform(all)).
object(output1_color8_t5_l3_b10_r3_w1_h6_mass6_shapeRectangle_scalex1_scaley6, transform(all)).
object(output1_color8_t1_l10_b4_r10_w1_h4_mass4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output1_color8_t1_l8_b4_r8_w1_h4_mass4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output1_color8_t1_l6_b4_r6_w1_h4_mass4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output1_color8_t1_l2_b4_r2_w1_h4_mass4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output1_color2_t11_l1_b11_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output1_color2_t5_l1_b5_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).

% Example 2 input grid_width10_height14
object(input2_color8_t1_l7_b1_r7_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input2_color8_t1_l3_b1_r3_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input2_color2_t12_l10_b12_r10_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input2_color2_t8_l10_b8_r10_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input2_color2_t4_l10_b4_r10_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).

% Example 2 output grid_width10_height14
object(output2_color8_t12_l4_b14_r4_w1_h3_mass3_shapeRectangle_scalex1_scaley3, transform(all)).
object(output2_color8_t8_l5_b11_r5_w1_h4_mass4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output2_color8_t8_l1_b11_r1_w1_h4_mass4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output2_color8_t4_l6_b7_r6_w1_h4_mass4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output2_color8_t4_l2_b7_r2_w1_h4_mass4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output2_color8_t1_l7_b3_r7_w1_h3_mass3_shapeRectangle_scalex1_scaley3, transform(all)).
object(output2_color8_t1_l3_b3_r3_w1_h3_mass3_shapeRectangle_scalex1_scaley3, transform(all)).
object(output2_color2_t12_l10_b12_r10_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_color2_t8_l10_b8_r10_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_color2_t4_l10_b4_r10_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).

% Example 3 input grid_width12_height12
object(input3_color8_t10_l1_b10_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input3_color8_t7_l1_b7_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input3_color8_t3_l1_b3_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input3_color2_t12_l9_b12_r9_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input3_color2_t12_l5_b12_r5_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).

% Example 3 output grid_width12_height12
object(output3_color8_t10_l1_b10_r4_w4_h1_mass4_shapeRectangle_scalex4_scaley1, transform(all)).
object(output3_color8_t9_l5_b9_r8_w4_h1_mass4_shapeRectangle_scalex4_scaley1, transform(all)).
object(output3_color8_t8_l9_b8_r12_w4_h1_mass4_shapeRectangle_scalex4_scaley1, transform(all)).
object(output3_color8_t7_l1_b7_r4_w4_h1_mass4_shapeRectangle_scalex4_scaley1, transform(all)).
object(output3_color8_t6_l5_b6_r8_w4_h1_mass4_shapeRectangle_scalex4_scaley1, transform(all)).
object(output3_color8_t5_l9_b5_r12_w4_h1_mass4_shapeRectangle_scalex4_scaley1, transform(all)).
object(output3_color8_t3_l1_b3_r4_w4_h1_mass4_shapeRectangle_scalex4_scaley1, transform(all)).
object(output3_color8_t2_l5_b2_r8_w4_h1_mass4_shapeRectangle_scalex4_scaley1, transform(all)).
object(output3_color8_t1_l9_b1_r12_w4_h1_mass4_shapeRectangle_scalex4_scaley1, transform(all)).
object(output3_color2_t12_l9_b12_r9_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output3_color2_t12_l5_b12_r5_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
```


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 4 input grid_width17_height12
object(input4_color8_t11_l17_b11_r17_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input4_color8_t9_l17_b9_r17_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input4_color8_t6_l17_b6_r17_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input4_color8_t3_l17_b3_r17_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input4_color2_t12_l12_b12_r12_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input4_color2_t12_l7_b12_r7_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input4_color2_t12_l3_b12_r3_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).

% Example 4 output grid_width17_height12
PREDICT the lines that starts with object(output4_
```
Repeat the previous example prolog code, with the PREDICT replaced with your predictions.
There number of output rows may be different than the input rows.

---

Looking at the transformations in your examples, it seems that for each input rectangle, multiple output rectangles are generated with the same color and mass, but with increased width or height. For rectangles positioned vertically (height of 1), their height is multiplied by the number of rectangles of the same color in the input. For rectangles positioned horizontally (width of 1), their width is multiplied by the number of rectangles of the same color in the input.

Given these observations, here are the predicted outputs for Example 4:

```prolog
% Example 4 input grid_width17_height12
object(input4_color8_t11_l17_b11_r17_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input4_color8_t9_l17_b9_r17_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input4_color8_t6_l17_b6_r17_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input4_color8_t3_l17_b3_r17_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input4_color2_t12_l12_b12_r12_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input4_color2_t12_l7_b12_r7_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input4_color2_t12_l3_b12_r3_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).

% Example 4 output grid_width17_height12
object(output4_color8_t11_l14_b17_r14_w1_h4_mass4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output4_color8_t11_l11_b17_r11_w1_h4_mass4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output4_color8_t11_l8_b17_r8_w1_h4_mass4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output4_color8_t11_l5_b17_r5_w1_h4_mass4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output4_color8_t7_l14_b10_r14_w1_h4_mass4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output4_color8_t7_l11_b10_r11_w1_h4_mass4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output4_color8_t7_l8_b10_r8_w1_h4_mass4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output4_color8_t7_l5_b10_r5_w1_h4_mass4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output4_color8_t3_l14_b6_r14_w1_h4_mass4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output4_color8_t3_l11_b6_r11_w1_h4_mass4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output4_color8_t3_l8_b6_r8_w1_h4_mass4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output4_color8_t3_l5_b6_r5_w1_h4_mass4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output4_color2_t12_l12_b12_r15_w4_h1_mass4_shapeRectangle_scalex4_scaley1, transform(all)).
object(output4_color2_t12_l8_b12_r11_w4_h1_mass4_shapeRectangle_scalex4_scaley1, transform(all)).
object(output4_color2_t12_l4_b12_r7_w4_h1_mass4_shapeRectangle_scalex4_scaley1, transform(all)).
```

This prediction is based on the observed rules. The position of the rectangles and their numbers determine the size and position of the output rectangles. Notice how the color2 rectangles have increased width, and the color8 rectangles have increased height. The position of the output rectangles is also influenced by the position of the input rectangles.

