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  1. #1
    Join Date
    Apr 2012
    Location
    SW England
    Posts
    8,672

    Question Snowflake, Christmas Decoration or Tessellation?

    Don't spend too much time on this Challenge as "It's Christmas!".

    Challenge - Starting with an equilateral triangle, can you accurately recreate a Xara-solution to drawing the Koch Snowflake?
    Answer - no-one can as it is infinitely recursive.

    Here is my Snowflake:

    Click image for larger version. 

Name:	Snowlfake.png 
Views:	22 
Size:	71.6 KB 
ID:	123011

    As it is Christmas, here is my decoration:

    Click image for larger version. 

Name:	XmasDec.png 
Views:	18 
Size:	84.1 KB 
ID:	123012

    And finally, here is my plane tessellation:

    Click image for larger version. 

Name:	KochTessltn.jpg 
Views:	17 
Size:	89.4 KB 
ID:	123013

    To be clear, I want a set of steps allowing up to a fifth recursion.
    Each recursion simply involves replace the middle third of any current straight line with a path that adds two sides of a (one-third) smaller equilateral triangle:

    Click image for larger version. 

Name:	Koch Rule.png 
Views:	15 
Size:	3.3 KB 
ID:	123014

    Enjoy it without getting too gnarly.

    Acorn
    Acorn - My currently active Xara software: occasionally serviced XDPX, purposely unserviced XDPX12 & XDPX11 (32/64-bit), unserviced XWD Premium 15 & 12, XPGD10, X3D7 and lots of 'permanently-owned' licences back through time (to CC's Artworks)

  2. #2
    Join Date
    Nov 2018
    Location
    Italy
    Posts
    61

    Default Re: Snowflake, Christmas Decoration or Tessellation?

    Quote Originally Posted by Acorn View Post
    Don't spend too much time on this Challenge as "It's Christmas!".

    Challenge - Starting with an equilateral triangle, can you accurately recreate a Xara-solution to drawing the Koch Snowflake?
    Answer - no-one can as it is infinitely recursive.

    Here is my Snowflake:

    Click image for larger version. 

Name:	Snowlfake.png 
Views:	22 
Size:	71.6 KB 
ID:	123011

    As it is Christmas, here is my decoration:

    Click image for larger version. 

Name:	XmasDec.png 
Views:	18 
Size:	84.1 KB 
ID:	123012

    And finally, here is my plane tessellation:

    Click image for larger version. 

Name:	KochTessltn.jpg 
Views:	17 
Size:	89.4 KB 
ID:	123013

    To be clear, I want a set of steps allowing up to a fifth recursion.
    Each recursion simply involves replace the middle third of any current straight line with a path that adds two sides of a (one-third) smaller equilateral triangle:

    Click image for larger version. 

Name:	Koch Rule.png 
Views:	15 
Size:	3.3 KB 
ID:	123014

    Enjoy it without getting too gnarly.

    Acorn
    Sorry, but this time I'll be too drunk or busy eating everything to even understand the challenge... Marry Christmas to everyone here!
    Marco.

  3. #3
    Join Date
    Apr 2012
    Location
    SW England
    Posts
    8,672

    Default Re: Snowflake, Christmas Decoration or Tessellation?

    Marco, just make sure you try a Koch perimeter walk to get rid of the excesses.

    Acorn
    Acorn - My currently active Xara software: occasionally serviced XDPX, purposely unserviced XDPX12 & XDPX11 (32/64-bit), unserviced XWD Premium 15 & 12, XPGD10, X3D7 and lots of 'permanently-owned' licences back through time (to CC's Artworks)

  4. #4
    Join Date
    Nov 2018
    Location
    Italy
    Posts
    61

    Default Re: Snowflake, Christmas Decoration or Tessellation?

    I fear that won't still be enough...
    Marco.

  5. #5
    Join Date
    Nov 2018
    Location
    Italy
    Posts
    61

    Default Re: Snowflake, Christmas Decoration or Tessellation?

    Bye the way, here is my snowflake... feel free to zoom in. I've lost time of the iterations.

    Attachment 123018

    Sadly it has been resized to 800x930px...
    Attached Thumbnails Attached Thumbnails Click image for larger version. 

Name:	snowflake - Copia.jpg 
Views:	22 
Size:	58.2 KB 
ID:	123019  
    Marco.

  6. #6
    Join Date
    May 2002
    Location
    Canada
    Posts
    1,814

    Default Re: Snowflake, Christmas Decoration or Tessellation?

    .

  7. #7
    Join Date
    Apr 2012
    Location
    SW England
    Posts
    8,672

    Default Re: Snowflake, Christmas Decoration or Tessellation?

    Quote Originally Posted by behzad View Post
    .
    Is this a solution? Is it just stop? Did you zoom in and find the point?

    Merry Xmas.

    Acorn
    Acorn - My currently active Xara software: occasionally serviced XDPX, purposely unserviced XDPX12 & XDPX11 (32/64-bit), unserviced XWD Premium 15 & 12, XPGD10, X3D7 and lots of 'permanently-owned' licences back through time (to CC's Artworks)

 

 

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