Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]

Groups > sci.math > #603418

Re: A Lattice drawing challenge.

From "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups sci.math
Subject Re: A Lattice drawing challenge.
Date 2023-06-26 15:03 -0700
Organization A noiseless patient Spider
Message-ID <u7d1vp$13eeq$1@dont-email.me> (permalink)
References (2 earlier) <64bbd985-d571-4843-b312-5b9d201e7228n@googlegroups.com> <dfc445ed-844c-450d-9b33-063d8d020131n@googlegroups.com> <c5c37967-2d52-482a-8976-5103b495e214n@googlegroups.com> <bb15b959-c6ca-44fc-b476-4e5906bf1339n@googlegroups.com> <683f2e35-14a5-4612-84a7-24fd6656d76dn@googlegroups.com>

Show all headers | View raw

On 6/26/2023 2:56 PM, Dan joyce wrote:
> On Sunday, June 25, 2023 at 9:53:33 PM UTC-4, Dan joyce wrote:
>> On Sunday, June 25, 2023 at 8:25:21 PM UTC-4, Dan joyce wrote:
>>> On Sunday, June 25, 2023 at 4:47:27 PM UTC-4, Dan joyce wrote:
>>>> On Sunday, June 25, 2023 at 4:39:08 PM UTC-4, Dan joyce wrote:
>>>>> On Saturday, June 24, 2023 at 5:53:33 PM UTC-4, Chris M. Thomasson wrote:
>>>>>> On 6/23/2023 7:57 PM, Dan joyce wrote:
>>>>>>> A rectangular lattice of the first order with 10X11
>>>>>>> sides. 440 lines total.
>>>>>>> The challenge is to draw a lattice of this size that
>>>>>>> the pencil never leaves the paper and never retraces
>>>>>>> or crosses another line.
>>>>>>> Is it possible for an algorithm to generate the next
>>>>>>> larger one and so on by the information below on this
>>>>>>> one?
>>>>>>> I converted the directions to integers making it easier
>>>>>>> to spot a possible pattern but so far no luck.
>>>>>>>
>>>>>>> Right =1, Down =2, Left =3 and Up =4
>>>>>>> This one below has 440 separate lines that are drawn.
>>>>>>> A total of 200 completed cells.
>>>>>>>
>>>>>>> 1,4,3,2,3,4,1,4,1,2,1,4,3,4,1,2,1,2,3,2,3,2
>>>>>>> 1,4,1,4,1,4,3,4,3,4,3,2,3,2,3,2,3,2,1,2,3,4
>>>>>>> 3,4,1,4,1,4,1,4,1,4,1,2,1,2,1,2,1,2,3,2,3,2
>>>>>>> 3,2,3,2,3,4,3,2,1,2,1,4,1,4,1,4,1,4,1,4,1,4
>>>>>>> 3,4,3,4,3,4,3,4,3,2,3,2,3,2,3,2,3,2,3,2,1,2
>>>>>>> 1,2,3,4,3,4,3,4,1,4,1,4,1,4,1,4,1,4,1,4,1,2
>>>>>>> 1,2,1,2,1,2,1,2,1,2,3,2,3,2,3,2,3,2,3,2,3,2
>>>>>>> 3,2,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,3,4,3,4
>>>>>>> 3,4,3,4,3,4,3,4,3,2,3,2,3,2,3,2,3,2,3,2,3,2
>>>>>>> 3,2,1,2,1,2,1,2,1,2,1,2,3,4,3,4,3,4,3,4,3,4
>>>>>>> 3,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,2,1,2
>>>>>>> 1,2,1,2,1,2,1,2,1,2,1,2,3,2,3,2,3,2,3,2,3,2
>>>>>>> 3,2,3,2,3,2,3,4,3,2,1,2,1,4,1,4,1,4,1,4,1,4
>>>>>>> 1,4,1,4,1,4,1,4,1,4,3,4,3,4,3,4,3,4,3,4,3,4
>>>>>>> 3,4,3,4,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2
>>>>>>> 3,2,1,2,1,2,1,2,1,2,1,2,1,2,3,4,3,4,3,4,3,4
>>>>>>> 3,4,3,4,3,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4
>>>>>>> 1,4,1,4,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2
>>>>>>> 1,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2
>>>>>>> 3,4,3,4,3,4,1,4,1,4,3,4,3,4,1,4,1,2,1,4,3,4
>>>>>>>
>>>>>>> To the left of the bottom corner is the inward
>>>>>>> path going roughly straight in to the center
>>>>>>> of the lattice but not quite to the center.
>>>>>>> All previous lattices that are smaller have
>>>>>>> the same but shorter path depending on their
>>>>>>> size. As each lattice gets larger the path
>>>>>>> grows longer but maintains roughly the same
>>>>>>> position on the lattice.
>>>>>>> So the challenge is, who can produce a algorithm
>>>>>>> to produce larger and larger lattices then the one
>>>>>>> above?
>>>>>>> I can produce them but only by the observation of
>>>>>>> the previous lattice. So no algorithm is involved.
>>>>>>> It is quite possible someone will come up with an
>>>>>>> algorithm that could theoretically produce these
>>>>>>> larger and larger lattices --->oo
>>>>>>>
>>>>>>> Happy coding!
>>>>>> I might have some free time to work on it again. Been busy lately. Here
>>>>>> is some music that might go with the animated building process:
>>>>>>
>>>>>> https://youtu.be/9Sbvylpwah8?t=29
>>>>>>
>>>>>> ;^)
>>>>> Chris, is there anything out there that's documented that's
>>>>> generates square lattice's from just a 2 sided, 3 sided, 4 sided, 5 sided, to --->oo sided
>>>>> lattices without lifting the pencil or retracing a line or crossing a line?
>>>>> If there is then I am just reinventing the wheel.
>>>>> Anyone else that can direct me to that documentation I would appreciate it.
>>>>> This is not counting the first one I proposed where it created --->oo pathway
>>>>> only on its return to the origin it produced the cells. This is different, it produces
>>>>> the cells on the way out and finishes the lattice on a slowly developing pathway
>>>>> that gets filled to produce the desired size of the square lattice.
>>>>> The triangular lattice where the long side has one more cell than the short side where
>>>>> that pathway grows longer for each larger lattice to complete then these square lattices.
>>>>>
>>>>> Dan '
>>>> So basically it means the pathways in these square lattices grow in length at a slower >rate between larger and larger lattices then the rectangular lattices do.
>>> Still searching for something even close to my current proposal about square lattices
>>> being drawn without lifting the pencil or retracing a line or crossing a line and building
>>> these lattices, hypothetically, in numbers --->oo
>>> Or sides, hypothetically, --->oo in length.
>>> Anyone else find anything close?
>>> If no responses in a few days I will post 5 of the first few square lattices using the
>>> integer code for each of the 4 directions. Right = 1, Down = 2, Left = 3, and Up = 4.
>> Ah, what the heck, I can't find anything that closely resembles what I propose
>> about square lattices.
>> The finale listing on square lattices starting with just a twosided lattice
>> where the pencil never leaves the paper in that there is no retrace or crossing
>> another line.
>> Each line drawn is followed by another at a right or left 90 degree turn.
>> The first two sided square lattice then the 2d 3 sided square lattice and then the 3rd.
>> 4 sided square lattice and then the 4th 5 sided square lattice.
>> Where all the rest can be produced, theoretically, with an algorithm --->oo
>> I havn't figured out the algorithm but if I don't I am sure somone will.
>>
>> Right =1,Down =2,Left =3, Up = 4
>> --------------------------------
>> A 2 sided square lattice.
>> 1,2,3,2,3,4,3,4,1,2,1,4,3,4,1,2
>>
>> A 3 sided square lattice.
>> 1,2,3,2,3,4,3,4,1,2,1,4,3,4,3,2,3,2,1,2,1,2,1,4,1,4,1,4,3,4,3,4,3,2,1,2
>>
>> A 4 sided square lattice.
>> 1,2,3,2,3,4,3,4,1,2,1,4,3,4,3,2,3,2,1,2,1,2,1,4,1,4,1,4,3,4,3,4,3,4,1,2,1,2,1,2,1,2,3,2
>> 3,2,3,2,3,4,3,4,3,4,3,4,1,4,1,4,1,2,1,2
>>
>> A 5 sided square lattice.
>> 1,2,3,2,3,4,3,4,1,2,1,4,3,4,3,2,3,2,1,2,1,2,1,4,1,4,1,4,3,4,3,4,3,4,1,2,1,2,1,2,1,2,3,2
>> 3,2,3,2,3,4,3,4,3,4,3,4,1,4,1,4,3,2,3,2,3,2,1,2,1,2,1,2,1,2,1,4,1,4,1,4,1,4,1,4,3,4,3,4
>> 3,4,3,4,3,2,3,2,1,2,1,2
>>
>> A 6 sided square lattice.
>> 1,2,3,2,3,4,3,4,1,2,1,4,3,4,3,2,3,2,1,2,1,2,1,4,1,4,1,4,3,4,3,4,3,4,1,2,1,2,1,2,1,2,3,2
>> 3,2,3,2,3,4,3,4,3,4,3,4,1,4,1,4,3,2,3,2,3,2,1,2,1,2,1,2,1,2,1,4,1,4,1,4,1,4,1,4,3,4,3,4
>> 3,4,3,4,3,2,3,4,1,4,1,2,1,2,1,2,1,2,1,2,1,2,3,2,3,2,3,2,3,2,3,2,3,4,3,4,3,4,3,4,3,4,3,4
>> 1,4,1,4,1,4,1,2,1,2,1,2
>> Notice that each larger and larger lattice copies almost all the previous data from
>> the previous lattice and then continues on to complete its own larger lattice.
>> The only difference is the previous lattice fills the short pathway to complete the
>> square lattice for that lattice.
>>
>> Also the ratio between each succeeding lattice have very short continued fractions.
>> Increasing slowly in length and a smaller and smaller ratio between each total number
>> of terms between each succeeding lattice.
>> Dan
> Aha! I did reinvented the lattice drawing without lifting the pencil and it took
> Bard (AI) to tell me. So for now, aside from mistakes, now an then it can
> become a useful tool.
> 
> Hilbert curve:
> Bard 's answer to my question about drawing a lattice without lifting the pencil.
> Bard's answer---
> Start at a point in the plane.
> Move your pencil one unit to the right.
> Turn 90 degrees counterclockwise.
> Move your pencil one unit up.
> Turn 90 degrees counterclockwise.
> Move your pencil one unit to the left.
> Turn 90 degrees counterclockwise.
> Move your pencil one unit down.
> Repeat steps 2-8 until you have reached the desired size of the lattice.
> The Hilbert curve is a very efficient way to draw a lattice, and it can be used to create lattices of any size. However, it is important to note that the Hilbert curve is not the only way to draw a lattice without lifting the pencil. There are other methods that can be used, and the best method to use will depend on the specific size and shape of the lattice that you want to draw.
> 
> 

I am getting fonder of the never ending triangle that expands 
forevermore on the x and y axes:

https://i.ibb.co/zVfMJkH/image.png

Back to sci.math | Previous | Next — Previous in thread | Next in thread | Find similar | Unroll thread

Thread

A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-23 19:57 -0700
  Re: A Lattice drawing challenge. Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2023-06-23 20:44 -0700
    Re: A Lattice drawing challenge. Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2023-06-23 22:34 -0700
      Re: A Lattice drawing challenge. Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2023-06-24 00:01 -0700
        Re: A Lattice drawing challenge. Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2023-06-24 00:54 -0700
    Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-24 05:25 -0700
      Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-24 05:56 -0700
        Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-24 06:16 -0700
          Re: A Lattice drawing challenge. Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2023-06-24 11:39 -0700
            Re: A Lattice drawing challenge. Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2023-06-24 12:08 -0700
            Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-24 16:56 -0700
  Re: A Lattice drawing challenge. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-24 14:53 -0700
    Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-24 16:42 -0700
    Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-25 13:39 -0700
      Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-25 13:47 -0700
        Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-25 17:25 -0700
          Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-25 18:53 -0700
            Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-26 14:56 -0700
              Re: A Lattice drawing challenge. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-26 15:03 -0700
                Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-26 15:15 -0700
                Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-26 16:10 -0700
                Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-26 16:57 -0700
                Re: A Lattice drawing challenge. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-27 11:58 -0700
                Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-27 17:31 -0700
                Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-27 17:48 -0700
                Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-26 17:00 -0700
                Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-26 18:46 -0700
                Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-26 20:52 -0700
                Re: A Lattice drawing challenge. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-28 17:19 -0700
                Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-29 19:30 -0700
                Re: A Lattice drawing challenge. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-29 19:53 -0700
                Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-08-08 05:54 -0700
                Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-08-08 11:06 -0700
  Re: A Lattice drawing challenge. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-27 21:20 -0700
    Re: A Lattice drawing challenge. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-27 21:27 -0700
      Re: A Lattice drawing challenge. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-27 21:36 -0700
  Re: A Lattice drawing challenge. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-27 21:45 -0700
    Re: A Lattice drawing challenge. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-27 21:46 -0700
      Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-27 21:51 -0700
        Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-27 21:58 -0700
          Re: A Lattice drawing challenge. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-27 22:18 -0700
            Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-27 22:20 -0700
              Re: A Lattice drawing challenge. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-27 22:21 -0700
                Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-27 22:34 -0700
                Re: A Lattice drawing challenge. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-27 23:03 -0700
                Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-28 03:58 -0700
                Re: A Lattice drawing challenge. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-28 12:51 -0700
                Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-28 16:36 -0700
                Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-28 16:46 -0700
          Re: A Lattice drawing challenge. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-27 22:20 -0700
      Re: A Lattice drawing challenge. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-27 22:12 -0700
      Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-27 22:14 -0700
    Re: A Lattice drawing challenge. Dan joyce <danj4084@gmail.com> - 2023-06-28 04:46 -0700
  Re: A Lattice drawing challenge. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-28 00:19 -0700

csiph-web