Simple Fractal square

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I am working on a math question about infinite series, and one of the question images is below.

iterations of subdividing a square

Each new white square has an area that is 1/4 of the previous square.

Always looking to learn elegant ways to create things using Mathematica, and in this case, probably recursion as well?

I know it's not complicated, but any help with the process would be appreciated.

Having a NICE diagram really helps with creating a better response.
(questions about sums of areas of white, black, etc.)

asked 1 hour ago

Tom De Vries

1,6351224

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up vote
3
down vote

favorite

I am working on a math question about infinite series, and one of the question images is below.

iterations of subdividing a square

Each new white square has an area that is 1/4 of the previous square.

Always looking to learn elegant ways to create things using Mathematica, and in this case, probably recursion as well?

I know it's not complicated, but any help with the process would be appreciated.

Having a NICE diagram really helps with creating a better response.
(questions about sums of areas of white, black, etc.)

asked 1 hour ago

Tom De Vries

1,6351224

add a commentÂ |Â

up vote
3
down vote

favorite

I am working on a math question about infinite series, and one of the question images is below.

iterations of subdividing a square

Each new white square has an area that is 1/4 of the previous square.

Always looking to learn elegant ways to create things using Mathematica, and in this case, probably recursion as well?

I know it's not complicated, but any help with the process would be appreciated.

Having a NICE diagram really helps with creating a better response.
(questions about sums of areas of white, black, etc.)

asked 1 hour ago

Tom De Vries

1,6351224

I am working on a math question about infinite series, and one of the question images is below.

iterations of subdividing a square

Each new white square has an area that is 1/4 of the previous square.

Always looking to learn elegant ways to create things using Mathematica, and in this case, probably recursion as well?

I know it's not complicated, but any help with the process would be appreciated.

Having a NICE diagram really helps with creating a better response.
(questions about sums of areas of white, black, etc.)

graphics recursion iteration

asked 1 hour ago

Tom De Vries

1,6351224

asked 1 hour ago

Tom De Vries

1,6351224

asked 1 hour ago

Tom De Vries

1,6351224

asked 1 hour ago

Tom De Vries

1,6351224

asked 1 hour ago

Tom De Vries

1,6351224

add a commentÂ |Â

2 Answers
2

active

oldest

votes

up vote
3
down vote

coords = 0, 0, 0, 1, 1, 1, 1, 0;
tf = Composition[TranslationTransform[1/2, 0], ScalingTransform[1/2, 1/2]]
rects = NestList[tf /@ ## &, coords, 4];
Graphics[ EdgeForm[Black], Rectangle,
FaceForm[Gray], Polygon@#, FaceForm[White], Polygon@#2 & @@@ 
Transpose[rects, Most /@ rects], FaceForm[White], Polygon[Last@rects]]

enter image description here

edited 4 mins ago

answered 14 mins ago

kglr

167k8188390

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up vote
1
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n = 100;
T1 = Developer`ToPackedArray[-1., 0., -0.5, 0., -0.5, 0.5];
T2 = Developer`ToPackedArray[-0.5, 0.5, 0., 0.5, 0., 1.];
Graphics[
 Polygon[Table[0.5^k T1, k, 0, n]],
 Polygon[Table[0.5^k T2, k, 0, n]]
 ]

enter image description here

answered 6 mins ago

Henrik Schumacher

42.8k261127

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2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

up vote
3
down vote

coords = 0, 0, 0, 1, 1, 1, 1, 0;
tf = Composition[TranslationTransform[1/2, 0], ScalingTransform[1/2, 1/2]]
rects = NestList[tf /@ ## &, coords, 4];
Graphics[ EdgeForm[Black], Rectangle,
FaceForm[Gray], Polygon@#, FaceForm[White], Polygon@#2 & @@@ 
Transpose[rects, Most /@ rects], FaceForm[White], Polygon[Last@rects]]

enter image description here

edited 4 mins ago

answered 14 mins ago

kglr

167k8188390

add a commentÂ |Â

up vote
3
down vote

coords = 0, 0, 0, 1, 1, 1, 1, 0;
tf = Composition[TranslationTransform[1/2, 0], ScalingTransform[1/2, 1/2]]
rects = NestList[tf /@ ## &, coords, 4];
Graphics[ EdgeForm[Black], Rectangle,
FaceForm[Gray], Polygon@#, FaceForm[White], Polygon@#2 & @@@ 
Transpose[rects, Most /@ rects], FaceForm[White], Polygon[Last@rects]]

enter image description here

edited 4 mins ago

answered 14 mins ago

kglr

167k8188390

add a commentÂ |Â

up vote
3
down vote

coords = 0, 0, 0, 1, 1, 1, 1, 0;
tf = Composition[TranslationTransform[1/2, 0], ScalingTransform[1/2, 1/2]]
rects = NestList[tf /@ ## &, coords, 4];
Graphics[ EdgeForm[Black], Rectangle,
FaceForm[Gray], Polygon@#, FaceForm[White], Polygon@#2 & @@@ 
Transpose[rects, Most /@ rects], FaceForm[White], Polygon[Last@rects]]

enter image description here

edited 4 mins ago

answered 14 mins ago

kglr

167k8188390

coords = 0, 0, 0, 1, 1, 1, 1, 0;
tf = Composition[TranslationTransform[1/2, 0], ScalingTransform[1/2, 1/2]]
rects = NestList[tf /@ ## &, coords, 4];
Graphics[ EdgeForm[Black], Rectangle,
FaceForm[Gray], Polygon@#, FaceForm[White], Polygon@#2 & @@@ 
Transpose[rects, Most /@ rects], FaceForm[White], Polygon[Last@rects]]

enter image description here

edited 4 mins ago

answered 14 mins ago

kglr

167k8188390

edited 4 mins ago

answered 14 mins ago

kglr

167k8188390

answered 14 mins ago

kglr

167k8188390

answered 14 mins ago

kglr

167k8188390

add a commentÂ |Â

up vote
1
down vote

n = 100;
T1 = Developer`ToPackedArray[-1., 0., -0.5, 0., -0.5, 0.5];
T2 = Developer`ToPackedArray[-0.5, 0.5, 0., 0.5, 0., 1.];
Graphics[
 Polygon[Table[0.5^k T1, k, 0, n]],
 Polygon[Table[0.5^k T2, k, 0, n]]
 ]

enter image description here

answered 6 mins ago

Henrik Schumacher

42.8k261127

add a commentÂ |Â

up vote
1
down vote

n = 100;
T1 = Developer`ToPackedArray[-1., 0., -0.5, 0., -0.5, 0.5];
T2 = Developer`ToPackedArray[-0.5, 0.5, 0., 0.5, 0., 1.];
Graphics[
 Polygon[Table[0.5^k T1, k, 0, n]],
 Polygon[Table[0.5^k T2, k, 0, n]]
 ]

enter image description here

answered 6 mins ago

Henrik Schumacher

42.8k261127

add a commentÂ |Â

up vote
1
down vote

n = 100;
T1 = Developer`ToPackedArray[-1., 0., -0.5, 0., -0.5, 0.5];
T2 = Developer`ToPackedArray[-0.5, 0.5, 0., 0.5, 0., 1.];
Graphics[
 Polygon[Table[0.5^k T1, k, 0, n]],
 Polygon[Table[0.5^k T2, k, 0, n]]
 ]

enter image description here

answered 6 mins ago

Henrik Schumacher

42.8k261127

n = 100;
T1 = Developer`ToPackedArray[-1., 0., -0.5, 0., -0.5, 0.5];
T2 = Developer`ToPackedArray[-0.5, 0.5, 0., 0.5, 0., 1.];
Graphics[
 Polygon[Table[0.5^k T1, k, 0, n]],
 Polygon[Table[0.5^k T2, k, 0, n]]
 ]

enter image description here

answered 6 mins ago

Henrik Schumacher

42.8k261127

answered 6 mins ago

Henrik Schumacher

42.8k261127

answered 6 mins ago

Henrik Schumacher

42.8k261127

answered 6 mins ago

Henrik Schumacher

42.8k261127

add a commentÂ |Â

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