# File:Hilbert Curve - 6.webm

Hilbert_Curve_-_6.webm(WebM audio/video file, VP8, length 51 s, 360 × 360 pixels, 111 kbps overall)

## Summary

 Description English: Hilbert Curve at its sixth iteration Date 23 July 2013, 21:04:57 Source Own work Author CalmWords

VectorRotater[{x_, y_}, \[Theta]_, {x0_,

```  y0_}] := ({{Cos[\[Theta]], -Sin[\[Theta]]}, {Sin[\[Theta]],
Cos[\[Theta]]}}.Transpose[{{x, y} - {x0, y0}}] + {x0, y0}) //
Flatten
```

VectorScaler[{x_, y_}, r_, {x0_, y0_}] :=

``` r*({x - x0, y - y0}) + {x0, y0};
```

HilbertCurve[n_] := (

``` HilbertCurve[n] =
If[n == 1,
{{1/4, 1/4}, {1/4, 3/4}, {3/4, 3/4}, {3/4, 1/4}},
prev = HilbertCurve[n - 1];
scaledPrev = VectorScaler[#, 1/2, {1/2, 1/2}] & /@ prev;
scaledPrevRot1 =
Reverse[VectorRotater[#, \[Pi]/2, {1/2, 1/2}] & /@ scaledPrev];
scaledPrevRot2 =
Reverse[VectorRotater[#, -\[Pi]/2, {1/2, 1/2}] & /@ scaledPrev];
Join[
{-1/4, -1/4} + # & /@ scaledPrevRot2,
{-1/4, 1/4} + # & /@ scaledPrev,
{1/4, 1/4} + # & /@ scaledPrev,
{1/4, -1/4} + # & /@ scaledPrevRot1]
]
)
```

## Licensing

I, the copyright holder of this work, hereby publish it under the following license:
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## File history

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Date/TimeThumbnailDimensionsUserComment
current02:06, 24 July 201351 s, 360 × 360 (694 KB)CalmWords (talk | contribs)User created page with UploadWizard
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