Tangram and its variants

[ColorfulGabrielsp138]

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

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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.

[Entity Valkyrie 2]

Better tiles:

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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.

[ColorfulGabrielsp138]

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!

[ColorfulGabrielsp138]

Work in progress

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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!

[Citation needed]

Please check this out:

EDIT: The Extended Tangram for Samaranch is here.

[ColorfulGabrielsp138]

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

[pcallahan]

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.

[pcallahan]

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 (569.85 KiB) Viewed 2047 times

If you drop some shapes (the square or maybe the parallelogram, which I never liked ) 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.)

[Entity Valkyrie 2]

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?

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!

[breaker's glider gun]

Can we please use these tiles?

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snip

sure:

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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.

[Citation needed]

The pattern below is the Extended Tangram for Samaranch.

Code: Select all

#C Extended Tangram for Samaranch
#C http://conwaylife.com/forums/viewtopic.php?p=218089#p218089
#C http://polypad.amplify.com/p/4LB2q9mQwv5YQ
x = 40, y = 40, rule = 12ColorMarkedLife
19.2C$18.C2EC$17.C4EC$16.C6EC$15.C8EC$14.C10EC$13.C12EC$12.C14EC$11.C
7I2C7SC$10.C7IC2RC7SC$9.C7IC4RC7SC$8.C7IC6RC7SC$7.C7IC8RC7SC$6.C7IC10R
C7SC$5.C7IC12RC7SC$4.C7IC14RC7SC$3.C4K4MC7J7NC8QC$2.CH4K4MGC6J6NCW8QF
C$.C2H4K4M2GC5J5NC2W8Q2FC$C3H4K4M3GC4J4NC3W8Q3FC$C3V4K4M4GC3J3NC4W8Q3F
C$.C2V4K4M5GC2J2NC5W8Q2FC$2.CV4K4M6GCJNC6W8QFC$3.C4K4M7G2C7W8QC$4.C15U
15OC$5.C14U14OC$6.C13U13OC$7.C12U12OC$8.C11U11OC$9.C10U10OC$10.C9U9OC
$11.C8U8OC$12.C7U7OC$13.C6U6OC$14.C5U5OC$15.C4U4OC$16.C3U3OC$17.C2U2O
C$18.CUOC$19.2C!
[[ Z 10 COLOR 4 255 204 255 COLOR 6 153 85 255 COLOR 8 153 170 255 COLOR 22 255 85 187 COLOR 10 51 238 34 COLOR 13 34 136 238 COLOR 14 187 170 204 COLOR 17 238 136 34 COLOR 18 255 34 17 COLOR 20 204 170 187 ]]