I posted the shamrock challenge on 3/2/2012 and received this response from
David Ward Lambert on 3/12/2012. It has caused me to delve into polar
graphs which is a little premature for these challenges. But it has been
great fun and I've changed how I think about lots of things. I recommend
this strange post as well as Tau Day posts on Google:
http://laughingsquid.com/pi-is-wrong/
What he did was to find the "inside" of a trifolium, or three petal rose in
polar coordinates. It is essentially how you would "paint" the trifolium.
He said I could share this with everyone, and I didn't want to post it until
there were some options which "painted" the inside of a circle.
So I hope you will enjoy his masterful approach to a celebration of St.
Patrick's Day.
Linda
-----Original Message-----
From: David Ward Lambert [mailto:[email protected]]
Sent: Friday, March 02, 2012 2:43 PM
To: [email protected]
Subject: Shamrock solution.
NB. Save message or attachment as a script.
NB. Run on 80 width and height terminal with, roughly, NB.
-----------------------------------
NB. shell_prompt$ jconsole shamrock_dwl.ijs NB.
-----------------------------------
NB. Not bad in jgtk except that the final plot doesn't work.
NB. Works in jhs---remove the final line, exit 0l
TAU=: 2p1 NB. http://laughingsquid.com/pi-is-wrong/
range=: 1&$: : (* (%~ i.))
radian_range=: TAU&range
grid_cartesian=: 2&$: : ({@:(# <@:(%~ i:))) NB. returns delightful boxes
NB. create_round_mask radius returns Boolean square array, 1 within circle
NB. create_round_mask result depends on comparison tolerance, 9!:18,
9!:19
create_round_mask=: (1-1e_14) >: |@:j./@>@:grid_cartesian
NB. 1j1&#&.|: is slow and fat
expand_for_character_cell_display=: 1j1&#"1
Gft_dwl=: 1 : 0
5 m Gft_dwl y
:
TOP_VIEW_TREE=.((create_round_mask x)})(m&,:)y{~(2#>:+:x)?@:$(#y)
expand_for_character_cell_display TOP_VIEW_TREE
)
smoutput ,.'Big GFT';BIG_GFT=: 8' 'Gft_dwl'/|\O'
smoutput ,.'Moonlit lemon tree';LEMON_TREE_AT_NIGHT=: 5'.'Gft_dwl'/|\o'
smoutput ,.'Underbearing carambola';PARCHED_STAR_FRUIT=: 5'
'Gft_dwl'*',3#'/|\'
trifolium=: 0&$: : (4 : 0) NB. trifolium radians
ROTATION=: 3 * x
PHI=. y
R=. ROTATION (1 o. ] p.~ 3 ,~ [) PHI
R *"1 (2 1 o./PHI)
)
create_shamrock_mask=: 0&$: : (4 : 0)"0 NB. rotation create_shamrock_mask
half_size GRID=. i:1 j. y RADIAL_DENSITY=. 8 NB. An adjective would help to
free these parameters OUTLINE_DENSITY=. 555 T=. x trifolium radian_range
OUTLINE_DENSITY
FR=. range RADIAL_DENSITY NB. radial factors
FR=. %:@:(+ 0&=) FR NB. square root makes the bigger factors closer.
The hook merely substitutes a 1 for the 0 INDEXES=. ~. <"1 ,/ |: GRID I.
T*/FR
1 INDEXES } 0 $~ 2 # >: y
)
NB. in following sentence 37 is roughly the half width of the final shamrock
and 0.2 controls leaf size smoutput ,.'St.
Pat';expand_for_character_cell_display ' X'{~+./ (1
_1*0.2) create_shamrock_mask 37
smoutput'If you replace the 3s in trifolium with 4, does the code draw a
lucky clover?'
smoutput'See comments about global comparison tolerance.'
load'plot'
plot ;/ trifolium radian_range 100
exit 0
NB. Save message as script sham_dwl.ijs
NB. Run from 80 width terminal with
NB. -----------------------------------
NB. shell_prompt$ jconsole sham_dwl.ijs
NB. -----------------------------------
TAU=: 2p1 NB. http://laughingsquid.com/pi-is-wrong/
range=: 1&$: : (* (%~ i.))
radian_range=: TAU&range
grid_cartesian=: 2&$: : ({@:(# <@:(%~ i:))) NB. returns delightful boxes
NB. create_round_mask radius returns Boolean square array, 1 within circle
NB. create_round_mask result depends on comparison tolerance, 9!:18, 9!:19
create_round_mask=: (1-1e_14) >: |@:j./@>@:grid_cartesian
NB. 1j1&#&.|: is slow and fat
expand_for_character_cell_display=: 1j1&#"1
Gft_dwl=: 1 : 0
5 m Gft_dwl y
:
TOP_VIEW_TREE=.((create_round_mask x)})(m&,:)y{~(2#>:+:x)?@:$(#y)
expand_for_character_cell_display TOP_VIEW_TREE
)
smoutput ,.'Big GFT';BIG_GFT=: 8' 'Gft_dwl'/|\O'
smoutput ,.'Moonlit lemon tree';LEMON_TREE_AT_NIGHT=: 5'.'Gft_dwl'/|\o'
smoutput ,.'Underbearing carambola';PARCHED_STAR_FRUIT=: 5' 'Gft_dwl'*',3#'/|\'
trifolium=: 0&$: : (4 : 0) NB. trifolium radians
ROTATION=: 3 * x
PHI=. y
R=. ROTATION (1 o. ] p.~ 3 ,~ [) PHI
R *"1 (2 1 o./PHI)
)
create_shamrock_mask=: 0&$: : (4 : 0)"0 NB. rotation create_shamrock_mask
half_size
GRID=. i:1 j. y
RADIAL_DENSITY=. 8 NB. An adjective would help to free these parameters
OUTLINE_DENSITY=. 555
T=. x trifolium radian_range OUTLINE_DENSITY
FR=. range RADIAL_DENSITY NB. radial factors
FR=. %:@:(+ 0&=) FR NB. square root makes the bigger factors closer. The hook
merely substitutes a 1 for the 0
INDEXES=. ~. <"1 ,/ |: GRID I. T*/FR
1 INDEXES } 0 $~ 2 # >: y
)
NB. in following sentence 37 is roughly the half width of the final shamrock
and 0.2 controls leaf size
smoutput ,.'St. Pat';expand_for_character_cell_display ' X'{~+./ (1 _1*0.2)
create_shamrock_mask 37
smoutput'If you replace the 3s in trifolium with 4, does the code draw a lucky
clover?'
smoutput'See comments about global comparison tolerance.'
load'plot'
plot ;/ trifolium radian_range 100
exit 0
----------------------------------------------------------------------
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