Tangram and its variants

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ColorfulGabrielsp138
Posts: 288
Joined: March 29th, 2021, 5:45 am

Tangram and its variants

Post by ColorfulGabrielsp138 » June 18th, 2021, 9:01 am

This thread is for discussing the famous Tangram puzzle and its variants.
The contents of this post is subject to change.

Code: Select all

x = 16, y = 8, rule = 12ColorMarkedLife
7I2.7O$6I.2E.6O$5I.4E.5O$4I.6E.4O$3I.4K.3S.3O$2I.H4KpA.3S.2O$I.2H4K2pA
.3S.O$.3H4K3pA.3S!
By the way, please don't delete this thread. Many of my threads on my previous account was now gone.

Code: Select all

x = 21, y = 21, rule = LifeColorful
11.E$10.3E$10.E.2E$13.E4$2.2B$.2B$2B$.2B15.2D$19.2D$18.2D$17.2D4$7.C$
7.2C.C$8.3C$9.C!
I have reduced the glider cost of quadratic growth to eight and probably to seven. Looking for conduits...

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Entity Valkyrie 2
Posts: 1756
Joined: February 26th, 2019, 7:13 pm
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Re: Tangram and its variants

Post by Entity Valkyrie 2 » June 18th, 2021, 10:19 pm

Better tiles:

Code: Select all

x = 152, y = 92, rule = 12ColorMarkedLife
7.C$6.CW$5.C2W$4.C3W$3.C4W$2.C5W$.C6W$C7W9$8S11.2C18.C7IC$8S10.C2EC
16.C7IC$8S9.C4EC14.C7IC$8S8.C6EC12.C7IC$8S7.C8EC10.C7IC$8S6.C10EC8.C
7IC$8S5.C12EC6.C7IC$8S4.C14EC4.C7IC9$7.C7pCC11.2C18.C7QC11.C$6.C7pCC
11.C2UC16.C7QC11.CpA$5.C7pCC11.C4UC14.C7QC11.C2pA$4.C7pCC11.C6UC12.C
7QC11.C3pA$3.C7pCC11.C8UC10.C7QC11.C4pA$2.C7pCC11.C10UC8.C7QC11.C5pA$
.C7pCC11.C12UC6.C7QC11.C6pA$C7pCC11.C14UC4.C7QC11.C7pA$7pCC12.C7U12.C
7Q12.8pA$6pCC14.C6U13.C6Q12.8pA$5pCC16.C5U14.C5Q12.8pA$4pCC18.C4U15.C
4Q12.8pA$3pCC20.C3U16.C3Q12.8pA$2pCC22.C2U17.C2Q12.8pA$pCC24.CU18.CQ
12.8pA$C26.C19.C12.8pA9$15.C11.2C11.8J75.C7XC11.2C$14.CO10.C2NC10.8J
74.C7XC11.C2TC$13.C2O9.C4NC9.8J73.C7XC11.C4TC$12.C3O8.C6NC8.8J72.C7XC
11.C6TC$11.C4O7.C8NC7.8J71.C7XC11.C8TC$10.C5O6.C10NC6.8J70.C7XC11.C
10TC$9.C6O5.C12NC5.8J69.C7XC11.C12TC$8.C7O4.C14NC4.8J68.C7XC11.C14TC$
7.C8O4.C14NC4.8J11.C8LC18.C15DC11.C7XC12.7T2C7T$6.C9O5.C12NC5.8J10.C
10LC16.C15DC11.C7XC13.6TC2.C6T$5.C10O6.C10NC6.8J9.C12LC14.C15DC11.C7X
C14.5TC4.C5T$4.C11O7.C8NC7.8J8.C14LC12.C15DC11.C7XC15.4TC6.C4T$3.C12O
8.C6NC8.8J7.C16LC10.C15DC11.C7XC16.3TC8.C3T$2.C13O9.C4NC9.8J6.C18LC8.
C15DC11.C7XC17.2TC10.C2T$.C14O10.C2NC10.8J5.C20LC6.C15DC11.C7XC18.TC
12.CT$C15O11.2C11.8J4.C22LC4.C15DC11.C7XC19.C14.C5$7.2C26.2C18.C12.C
7PC19.C26.C19.2C$6.C2RC24.C2FC16.CpB13.C7PC18.HC24.CV18.C2BC$5.C4RC
22.C4FC14.C2pB14.C7PC17.2HC22.C2V17.C4BC$4.C6RC20.C6FC12.C3pB15.C7PC
16.3HC20.C3V16.C6BC$3.C8RC18.C8FC10.C4pB16.C7PC15.4HC18.C4V15.C8BC$2.
C10RC16.C10FC8.C5pB17.C7PC14.5HC16.C5V14.C10BC$.C12RC14.C12FC6.C6pB
18.C7PC13.6HC14.C6V13.C12BC$C14RC12.C14FC4.C7pB19.C7PC12.7HC12.C7V12.
C14BC$7.C7RC11.C7FC12.C15pB12.8P4.C15H4.C15V4.C14BC$6.C7RC11.C7FC14.C
14pB12.8P5.C14H5.C14V5.C12BC$5.C7RC11.C7FC16.C13pB12.8P6.C13H6.C13V6.
C10BC$4.C7RC11.C7FC18.C12pB12.8P7.C12H7.C12V7.C8BC$3.C7RC11.C7FC20.C
11pB12.8P8.C11H8.C11V8.C6BC$2.C7RC11.C7FC22.C10pB12.8P9.C10H9.C10V9.C
4BC$.C7RC11.C7FC24.C9pB12.8P10.C9H10.C9V10.C2BC$C7RC11.C7FC26.C8pB12.
8P11.C8H11.C8V11.2C!
The state 3 diagonal edges must be overlapped, but the orthogonal edges must not overlap.
Bx222 IS MY WORST ENEMY.

Please click here for my own pages.

My recent rules:
StateInvestigator 3.0
B3-kq4ej5i6ckn7e/S2-i34q6a7
B3-kq4ej5y6c/S2-i34q5e
Move the Box

ColorfulGabrielsp138
Posts: 288
Joined: March 29th, 2021, 5:45 am

Re: Tangram and its variants

Post by ColorfulGabrielsp138 » July 28th, 2021, 6:02 am

SJW's "Sesquiominoes"

Code: Select all

x = 32, y = 32, rule = 12ColorMarkedLife
7.2C$6.C2UC$5.C4UC$4.C6UC$3.C8UC$2.C10UC$.C12UC$C14UC$C7U8pAC$.C6U9pA
C$2.C5U10pAC$3.C4U11pAC$4.C3U12pAC$5.C2U13pAC$6.CU14pAC$7.C15pAC$8.C7pC
C7QC$9.C7pCC7QC$10.C7pCC7QC$11.C7pCC7QC$12.C7pCC7QC$13.C7pCC7QC$14.C7pC
C7QC$15.C7pCC7QC$16.C7pC7QC$17.C6pC6QC$18.C5pC5QC$19.C4pC4QC$20.C3pC3Q
C$21.C2pC2QC$22.CpCQC$23.2C!

Code: Select all

x = 21, y = 21, rule = LifeColorful
11.E$10.3E$10.E.2E$13.E4$2.2B$.2B$2B$.2B15.2D$19.2D$18.2D$17.2D4$7.C$
7.2C.C$8.3C$9.C!
I have reduced the glider cost of quadratic growth to eight and probably to seven. Looking for conduits...

ColorfulGabrielsp138
Posts: 288
Joined: March 29th, 2021, 5:45 am

Re: Tangram and its variants

Post by ColorfulGabrielsp138 » August 14th, 2021, 5:49 am

Work in progress

Code: Select all

x = 68, y = 24, rule = 12ColorMarkedLife
8E.8E.C15K.C7G9.C15K$8E.8E.GC14K.QC6G9.GC14K$8E.8E.2GC13K.2QC5G9.2GC13K
$8E.8E.3GC12K.3QC4G9.3GC12K$8E.8E.4GC11K.4QC3G9.4GC11K$8E.8E.5GC10K.5Q
C2G9.5GC10K$8E.8E.6GC9K.6QCG9.6GC9K$8E.8E.7GC8K.7QC9.7GC8K$9.7GC9.C7K
.C7Q17.C7K$9.6GCI9.IC6K.OC6Q17.QC6K$9.5GC2I9.2IC5K.2OC5Q17.2QC5K$9.4G
C3I9.3IC4K.3OC4Q17.3QC4K$9.3GC4I9.4IC3K.4OC3Q17.4QC3K$9.2GC5I9.5IC2K.
5OC2Q17.5QC2K$9.GC6I9.6ICK.6OCQ17.6QCK$9.C7I9.7IC.7OC17.7QC$35.7OC17.
C7Q$35.6OCI17.IC6Q$35.5OC2I17.2IC5Q$35.4OC3I17.3IC4Q$35.3OC4I17.4IC3Q
$35.2OC5I17.5IC2Q$35.OC6I17.6ICQ$35.C7I17.7IC!

Code: Select all

x = 21, y = 21, rule = LifeColorful
11.E$10.3E$10.E.2E$13.E4$2.2B$.2B$2B$.2B15.2D$19.2D$18.2D$17.2D4$7.C$
7.2C.C$8.3C$9.C!
I have reduced the glider cost of quadratic growth to eight and probably to seven. Looking for conduits...

Citation needed
Posts: 173
Joined: April 1st, 2021, 1:03 am

Re: Tangram and its variants

Post by Citation needed » August 14th, 2021, 5:57 am

Please check this out:
Attachments
tangram.zip
Version 1.0
(3.88 KiB) Downloaded 73 times

ColorfulGabrielsp138
Posts: 288
Joined: March 29th, 2021, 5:45 am

Re: Tangram and its variants

Post by ColorfulGabrielsp138 » August 14th, 2021, 8:36 am

Is there a "Tangram holiday"? If not, maybe we could make today the "Tangram holiday".

Code: Select all

x = 21, y = 21, rule = LifeColorful
11.E$10.3E$10.E.2E$13.E4$2.2B$.2B$2B$.2B15.2D$19.2D$18.2D$17.2D4$7.C$
7.2C.C$8.3C$9.C!
I have reduced the glider cost of quadratic growth to eight and probably to seven. Looking for conduits...

User avatar
pcallahan
Posts: 845
Joined: April 26th, 2013, 1:04 pm

Re: Tangram and its variants

Post by pcallahan » August 14th, 2021, 11:02 am

I first saw tangram as a kid. I had a set and played around with making shapes, but I was never that excited by it. At the time I was also interested in origami and found its geometry more interesting (the similarity being that both use the geometry of dividing squares with 90° and 45° angles... and more for origami). The tile set strikes me as a little arbitrary, e.g. compared to Pentominoes, where the puzzle is defined by a complete set meeting combinatorial criteria (i.e. the 12 pentominoes). I.e., why do two kinds of right triangles repeat but the middle one is paired with a equal-area parallelogram? (So you can pack it into a square I guess, but it still seems like an arbitrary choice.)

Random thought: how about recursive tangrams in which the middle square is partitioned into tangrams? What kinds of shapes could you make? Not exactly fractals because the small parts would be limited to a small area. I'm not sure.

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pcallahan
Posts: 845
Joined: April 26th, 2013, 1:04 pm

Re: Tangram and its variants

Post by pcallahan » August 14th, 2021, 12:00 pm

You can dissect a right triangle or parallelogram as shown on the Wikipedia page. This gives a fully recursive Tangram tiling:
Screen Shot 2021-08-14 at 8.52.27 AM.png
Screen Shot 2021-08-14 at 8.52.27 AM.png (569.85 KiB) Viewed 1481 times
If you drop some shapes (the square or maybe the parallelogram, which I never liked :twisted:) then you should get a fractal along the lines of the Sierpinski carpet. Hausdorff dimension left as an exercise.

Inkscape tip: It is really easy to draw Tangram by snapping to midpoints. I draw the thick blue lines in Inkscape but stole the center dissections from wikipedia (I am tempted to redo the whole thin in Inkscape but I feel I have used up enough time already.)

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Entity Valkyrie 2
Posts: 1756
Joined: February 26th, 2019, 7:13 pm
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Re: Tangram and its variants

Post by Entity Valkyrie 2 » August 24th, 2021, 2:59 am

ColorfulGabrielsp138 wrote:
August 14th, 2021, 5:49 am
Work in progress

Code: Select all

x = 68, y = 24, rule = 12ColorMarkedLife
8E.8E.C15K.C7G9.C15K$8E.8E.GC14K.QC6G9.GC14K$8E.8E.2GC13K.2QC5G9.2GC13K
$8E.8E.3GC12K.3QC4G9.3GC12K$8E.8E.4GC11K.4QC3G9.4GC11K$8E.8E.5GC10K.5Q
C2G9.5GC10K$8E.8E.6GC9K.6QCG9.6GC9K$8E.8E.7GC8K.7QC9.7GC8K$9.7GC9.C7K
.C7Q17.C7K$9.6GCI9.IC6K.OC6Q17.QC6K$9.5GC2I9.2IC5K.2OC5Q17.2QC5K$9.4G
C3I9.3IC4K.3OC4Q17.3QC4K$9.3GC4I9.4IC3K.4OC3Q17.4QC3K$9.2GC5I9.5IC2K.
5OC2Q17.5QC2K$9.GC6I9.6ICK.6OCQ17.6QCK$9.C7I9.7IC.7OC17.7QC$35.7OC17.
C7Q$35.6OCI17.IC6Q$35.5OC2I17.2IC5Q$35.4OC3I17.3IC4Q$35.3OC4I17.4IC3Q
$35.2OC5I17.5IC2Q$35.OC6I17.6ICQ$35.C7I17.7IC!
Can we please use these tiles?
Entity Valkyrie 2 wrote:
June 18th, 2021, 10:19 pm

Code: Select all

x = 152, y = 92, rule = 12ColorMarkedLife
7.C$6.CW$5.C2W$4.C3W$3.C4W$2.C5W$.C6W$C7W9$8S11.2C18.C7IC$8S10.C2EC
16.C7IC$8S9.C4EC14.C7IC$8S8.C6EC12.C7IC$8S7.C8EC10.C7IC$8S6.C10EC8.C
7IC$8S5.C12EC6.C7IC$8S4.C14EC4.C7IC9$7.C7pCC11.2C18.C7QC11.C$6.C7pCC
11.C2UC16.C7QC11.CpA$5.C7pCC11.C4UC14.C7QC11.C2pA$4.C7pCC11.C6UC12.C
7QC11.C3pA$3.C7pCC11.C8UC10.C7QC11.C4pA$2.C7pCC11.C10UC8.C7QC11.C5pA$
.C7pCC11.C12UC6.C7QC11.C6pA$C7pCC11.C14UC4.C7QC11.C7pA$7pCC12.C7U12.C
7Q12.8pA$6pCC14.C6U13.C6Q12.8pA$5pCC16.C5U14.C5Q12.8pA$4pCC18.C4U15.C
4Q12.8pA$3pCC20.C3U16.C3Q12.8pA$2pCC22.C2U17.C2Q12.8pA$pCC24.CU18.CQ
12.8pA$C26.C19.C12.8pA9$15.C11.2C11.8J75.C7XC11.2C$14.CO10.C2NC10.8J
74.C7XC11.C2TC$13.C2O9.C4NC9.8J73.C7XC11.C4TC$12.C3O8.C6NC8.8J72.C7XC
11.C6TC$11.C4O7.C8NC7.8J71.C7XC11.C8TC$10.C5O6.C10NC6.8J70.C7XC11.C
10TC$9.C6O5.C12NC5.8J69.C7XC11.C12TC$8.C7O4.C14NC4.8J68.C7XC11.C14TC$
7.C8O4.C14NC4.8J11.C8LC18.C15DC11.C7XC12.7T2C7T$6.C9O5.C12NC5.8J10.C
10LC16.C15DC11.C7XC13.6TC2.C6T$5.C10O6.C10NC6.8J9.C12LC14.C15DC11.C7X
C14.5TC4.C5T$4.C11O7.C8NC7.8J8.C14LC12.C15DC11.C7XC15.4TC6.C4T$3.C12O
8.C6NC8.8J7.C16LC10.C15DC11.C7XC16.3TC8.C3T$2.C13O9.C4NC9.8J6.C18LC8.
C15DC11.C7XC17.2TC10.C2T$.C14O10.C2NC10.8J5.C20LC6.C15DC11.C7XC18.TC
12.CT$C15O11.2C11.8J4.C22LC4.C15DC11.C7XC19.C14.C5$7.2C26.2C18.C12.C
7PC19.C26.C19.2C$6.C2RC24.C2FC16.CpB13.C7PC18.HC24.CV18.C2BC$5.C4RC
22.C4FC14.C2pB14.C7PC17.2HC22.C2V17.C4BC$4.C6RC20.C6FC12.C3pB15.C7PC
16.3HC20.C3V16.C6BC$3.C8RC18.C8FC10.C4pB16.C7PC15.4HC18.C4V15.C8BC$2.
C10RC16.C10FC8.C5pB17.C7PC14.5HC16.C5V14.C10BC$.C12RC14.C12FC6.C6pB
18.C7PC13.6HC14.C6V13.C12BC$C14RC12.C14FC4.C7pB19.C7PC12.7HC12.C7V12.
C14BC$7.C7RC11.C7FC12.C15pB12.8P4.C15H4.C15V4.C14BC$6.C7RC11.C7FC14.C
14pB12.8P5.C14H5.C14V5.C12BC$5.C7RC11.C7FC16.C13pB12.8P6.C13H6.C13V6.
C10BC$4.C7RC11.C7FC18.C12pB12.8P7.C12H7.C12V7.C8BC$3.C7RC11.C7FC20.C
11pB12.8P8.C11H8.C11V8.C6BC$2.C7RC11.C7FC22.C10pB12.8P9.C10H9.C10V9.C
4BC$.C7RC11.C7FC24.C9pB12.8P10.C9H10.C9V10.C2BC$C7RC11.C7FC26.C8pB12.
8P11.C8H11.C8V11.2C!
Bx222 IS MY WORST ENEMY.

Please click here for my own pages.

My recent rules:
StateInvestigator 3.0
B3-kq4ej5i6ckn7e/S2-i34q6a7
B3-kq4ej5y6c/S2-i34q5e
Move the Box

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breaker's glider gun
Posts: 670
Joined: May 23rd, 2021, 10:26 am
Location: the inside of a stuffed anaconda or maybe [click to not expand]

Re: Tangram and its variants

Post by breaker's glider gun » December 22nd, 2021, 3:21 pm

Entity Valkyrie 2 wrote:
August 24th, 2021, 2:59 am
Can we please use these tiles?

Code: Select all

snip
sure:

Code: Select all

x = 32, y = 16, rule = 12ColorMarkedLife
15OC7I2C7W$14OC7IC2UC6W$13OC7IC4UC5W$12OC7IC6UC4W$11OC7IC8UC3W$10OC7I
C10UC2W$9OC7IC12UCW$8OC7IC14UC$7OC8LC7U8S$6OC10LC6U8S$5OC12LC5U8S$4OC
14LC4U8S$3OC16LC3U8S$2OC18LC2U8S$OC20LCU8S$C22LC8S!
those are great tiles.
:?: :?: . . . :!:
Give me a suggestion of something to draw here!

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