Log24

Friday, April 19, 2024

Benchmarking Meta.ai

Filed under: General — Tags: — m759 @ 10:15 pm

Transcription —

(With one correction The Meta.ai phrase "the  group of 322,560"
was changed to " group of 322,560" and one addition — the
acronym MOG was defined. Superscript numerals for missing footnotes
were removed.)

You

What is the Cullinane diamond theorem?

Meta AI

The Cullinane diamond theorem states that every image of D (a 4×4 array of two-color diagonally divided square tiles) under the group G (a group of 322,560 permutations of these 16 tiles) has some ordinary or color-interchange symmetry.

Here are some key points about the theorem :

  • The theorem is related to the Miracle Octad Generator (MOG) of R. T. Curtis and the Leech lattice.
     
  • The underlying geometry of the 4×4 patterns is closely related to the construction of the Steiner system S(5,8,24).
     
  • The theorem uses a simple decomposition technique for functions into a finite field.
     
  • The symmetry group of order 322,560 underlies both the diamond theorem figures and the square patterns of the MOG.
     
  • The theorem has applications in finite projective geometry and the study of symmetric patterns.

Graphic Design for Comedians:
The Old Carnegie Hall Joke

Filed under: General — Tags: , — m759 @ 12:07 pm

Related I Ching art —

For Harlan Kane and Jonathan Wingdings

Filed under: General — Tags: — m759 @ 10:08 am

http://m759.net/wordpress/?s="Design+Theory"

The Tortured Designers Department

Filed under: General — Tags: — m759 @ 9:23 am

"Who else decodes you?"Taylor Swift

Sunday, April 14, 2024

Benchmarking Pi

Filed under: General — Tags: , , — m759 @ 3:30 pm

An example of pi.ai's clear and pleasant conversational style
(output format simplified for presentation here) —


Can you help with computer coding problems?
 

Absolutely, Steven! 💻 While I can't guarantee I'll have all the answers, 
I'll certainly do my best to help you debug and find solutions to your 
coding conundrums. Which coding language are you working with, and what's 
giving you trouble?

 
I want to learn how Python can permute sections of a square array.
 

There are several ways to permute sections of a square array in Python, 
depending on your specific needs. Here are a few examples:

Using NumPy's random.permutation() function:

python

    import numpy as np

    arr = np.array([[1, 2], [3, 4]])
    permuted_arr = np.random.permutation(arr)

 

    Using itertools.permutations():

python

    import itertools

    arr = [[1, 2], [3, 4]]
    permutations = list(itertools.permutations(arr))

 

Using custom permutation algorithms:

python

    def custom_permutation(arr):
        # your custom permutation logic here

    arr = [[1, 2], [3, 4]]
    permuted_arr = custom_permutation(arr)

Each method has its own strengths and weaknesses, and which one 
you choose will depend on the size of your array, the number of 
permutations you need, and your performance requirements.


I would like to use python's custom permutation method to permute 
the four quadrants of a 4×4 array.

 
Here's an example of how to define a custom permutation function 
in Python to permute the four quadrants of a 4×4 array:
 
python

    def custom_permutation(arr):
        # Split array into 4 quadrants
        q1 = arr[:2, :2]
        q2 = arr[:2, 2:]
        q3 = arr[2:, :2]
        q4 = arr[2:, 2:]

        # Permute quadrants
        permuted_arr = np.block([
            [q3, q1],
            [q4, q2]
        ])

        return permuted_arr

    # Sample 4x4 array
    arr = np.array([[1, 2, 3, 4],
                    [5, 6, 7, 8],
                    [9, 10, 11, 12],
                    [13, 14, 15, 16]])

    permuted_arr = custom_permutation(arr)
    print(permuted_arr)

In this example, we've defined a function custom_permutation() 
that takes a 4×4 NumPy array as input. The function splits the array 
into four quadrants (q1, q2, q3, and q4), and then uses NumPy's block() 
function to create a new array with the quadrants permuted. The 
resulting permuted_arr array has its quadrants rearranged.

Of course, this is just one possible permutation of the array's quadrants. 
You can modify the custom_permutation() function to implement other 
permutations as needed.
 

I tried the code you gave me and got the error “np name not defined.”
 

Apologies for that! I missed an import statement in the previous example. 
You need to import the NumPy library at the beginning of your script to 
use the np alias and its functions. Here's the corrected code:
 
python

    import numpy as np

    def custom_permutation(arr):
        # Split array into 4 quadrants
        q1 = arr[:2, :2]
        q2 = arr[:2, 2:]
        q3 = arr[2:, :2]
        q4 = arr[2:, 2:]

        # Permute quadrants
        permuted_arr = np.block([
            [q3, q1],
            [q4, q2]
        ])

        return permuted_arr

    # Sample 4x4 array
    arr = np.array([[1, 2, 3, 4],
                    [5, 6, 7, 8],
                    [9, 10, 11, 12],
                    [13, 14, 15, 16]])

    permuted_arr = custom_permutation(arr)
    print(permuted_arr)

This code should work now without any issues.

It did work. Thank you, Pi. 

You're very welcome, Steven! I'm glad the code worked for you. 
If you have any more questions or need help with anything else, 
feel free to ask.

Recline in Peace . . .

Filed under: General — Tags: , — m759 @ 10:30 am

http://m759.net/wordpress/?s=Ringgold .

Wednesday, April 10, 2024

Hollywood Benchmark: The Blue Monkey* Diamond

Filed under: General — Tags: , — m759 @ 3:58 pm

* The name "Blue Monkey" is from a 2003 film. See also Hanuman
in this journal.
The image described by Vertex AI is from IMDb

Tuesday, March 21, 2023

Benchmarking Bard

Filed under: General — Tags: , , , — m759 @ 9:22 pm

Click to enlarge the above Google Bard remarks. 

A different Bard . . .

IMAGE- Opening of Wallace Stevens's Bard College speech, 1951

Thursday, November 18, 2021

Benchmarks

Filed under: General — Tags: , — m759 @ 5:22 pm

Wednesday, January 27, 2016

AI Benchmark

Filed under: General — Tags: — m759 @ 2:25 pm

Thursday, January 9, 2014

Digital Member

Filed under: General — Tags: , — m759 @ 11:00 am

Tuesday, September 7, 2010

Benchmark

Filed under: General — Tags: — m759 @ 2:02 am

September of 1957 was the month I entered high school. Also that month—

http://www.log24.com/log/pix10B/100907-Bench.jpg

    And so she did.

Related material: This journal on August 29, 2010, and the phrase "attention must be paid."

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