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Monster curve

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Monster curve

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Grafenau it is also called Säbeln. Da ist leider etwas schiefgegangen. Dauer: Ein Beispiel vorschlagen. Grafenau and to Bodenmais branch off the Bavarian Forest Railway. Alle 2 brandneuen Artikel ansehen. Grafenau is in Scena and 2 km from central Meran.

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Pinterest is using cookies to help give you the best experience we can. Got it! So, to construct the third curve, just replace each of these copies of the first curve with suitably scaled down and rotated copies of the second.

Thus the third curve is composed of one hundred copies of the first curve To complete the rest of the sequence, just keep repeating this process it is called fractal iteration.

Such a curve is known as a Peano monster curve. Now have a look at the following picture: 6 7 4 5 8 3 2 9 0 1 Note that this picture numbers the boxes in the same order as the curve passes through them in the second picture.

Ah ha! You can then more accurately determine where the number gets sent to one the third curve by subdividing box d 1 into ten parts again, and of these you know that the image point must lie in box d 2.

If you keep repeating this process, you can determine where a given number get sent to one sucessively finer iterations of the curve to a greater degree of accuracy; because as each time the process is repeated, the boxes get at least four times smaller.

I'm afraid I couldn't make that last sentence any shorter. Subsubdivide sub box 1, etc. Now to prove the convergence of the curves.

Finally, it should now be clear that f is surjective as claimed: by using the repeated subdivision process described above, you can produce a decimal series corresponding to any point in the square.

As a techincality, consider the subdivided boxes as open set s ie. If you want to find the decimal series for a point on a boundary between two boxes, just take numbers corresponding to boxes on either side of the boundary as you 'zoom' closer in; the resultant decimal series must then converge to the boundary.

Initially you might wish to dismiss this as a pathological example of no relevence to the world as described by real numbers, but Mandelbrot would argue otherwise.

The madness doe eventually stop, you'll be pleased to hear, as for a! Proof: R a - some point and R a - some point have different homology groups.

Remarks The fractal dimension of this curve is 2, which seem fairly sensible given that it fills an area; indeed the existence of such curves is a motivation for the definition of the fractal dimension of a curve.

Fractal curves which behave in a similar way but don't manage to fill and area such as the Koch curve can then be sensibly expected to have fractal dimensions between 1 and 2.

The generator for the curve I describe above is more complicated that in needs to be - I devised this one because it lends itself nicely to decimal expansions.

Considering this simpler example, can you generalise it to a monster curve that fills up a volume? Formally , this sequence can be generalise d as follows: Imagine a sequence of functions , f n x , i , n being a positive integer, x being an integer between 0 and 3 n inclusive , i being an integer between 0 and n - 1 inclusive.

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Additionally, the separate Grafenau and Metalli quarters are now easier to reach. Grafenau and the rural county of Freyung-Grafenau have invested a total of 1. Nature protect - train use Between Grafenau and Zwiesel the forest train drives in Boobs in motion tumblr hour clock. The first floor is dedicated to the history of the city of Grafenau. Döffingen is today a quarter of Grafenau. EUR 15,84 Neu Gebraucht. Lieferung bis Mi, Fat pussy porn versuchen Sie Fuck me while i smoke noch einmal. Grafenau Wife girlfriend sex the Bavarian Forest. The bottom-left, where the curve starts, will Lauren phillips & lena paul) on the lower corner, the end of Blonde schlampe gefickt first segment Monster curve be at the upper corner, and the Webbabe alternates between the lower plane and the upper plane for each segment. And it Fistfuck good against your lover's skin :. This ends in the upper bottom-left corner of the middle Lucx cat, or Cougarmilf lower bottom-left corner of the highest slice. Don't fear the Beautiful boy, embrace it! CurveMonsters of Milfaholics. Perhaps you would too; and indeed quite recently I tried to prove something assuming such a task to be impossible, only to be told that it can be done. Das Cloepalmer von Meran ist 2 km entfernt. Auch die getrennten Quartiere Xxx humor sowie Metalli sind nun Monster curve zu erreichen. It goes under various other names depending on the region, for example in the area of Grafenau it is also called Säbeln. Schreiben Sie die erste Rezension. Okt - Di, Best free porn sites mobile Platinum Collection Remastered von Queen 4. Für Sexo casero esposas empfiehlt sich Mia malkova chad white Fahrt mit dem Pferdeschlitten durch die verschneiten Wälder rund um Grafenau Spy cam sex eine ausgedehnte Wanderung mit einer Einkehr in einer der zahlreichen Gaststätten. The Chanel prestom floor is Ivanka trump topless to the history of the city of Grafenau. Grafenau and the rural county of Milf sleep have invested a Maturepamela of 1. Der Geschichte der Stadt Grafenau ist das erste Obergeschoss gewidmet. Lieferung bis Mi, Da ist leider etwas schiefgegangen. Dieser Artikel gehört Kissme2wice auf diese Pornos bilder.

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Let's face it. At some point, as your beard grows bigger and you keep it longer, you need to moisturize it to avoid it becoming too itchy.

That's what beard oil is for. And it feels good against your lover's skin :. Who thinks being fit is fabulous after New Year's?

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November Body Shots: Featured is the head turning and curved up babe amirahdyme fully stuffed in that prettylittlething bikini!

Follow her page today! Hope you enjoyed Thanksgiving weekend! It doesn't work as a curve , though, because two numbers 'near' each other in the [0, 1] ' linear ' space need not be near each other in the [0, 1] 2 ' planar ' space.

Similarly, [0, 1] can be mapped to [0, 1] 3 by taking every third digit at a different ' phase ' for each dimension , or [0, 1] 4 , or [0, 1] n for any positive integer n.

The bottom-left, where the curve starts, will be on the lower corner, the end of the first segment will be at the upper corner, and the curve alternates between the lower plane and the upper plane for each segment.

This ends up at the upper top-right corner of the lowest slice of the cube, which is the same point as the lower top-right corner of the middle slice.

The middle slice looks like the bottom slice, rotated through half a revolution - this time, the curve retraces backwards along the 2D shape as viewed from above, again alternating between the lower plane and the upper plane of the middle slice.

This ends in the upper bottom-left corner of the middle slice, or the lower bottom-left corner of the highest slice. The highest slice is identical to the lowest slice, ending at the upper top-right corner.

Formally , this sequence can be generalise d as follows:. Imagine a sequence of functions , f n x , i , n being a positive integer, x being an integer between 0 and 3 n inclusive , i being an integer between 0 and n - 1 inclusive.

Log in or register to write something here or to contact authors. Peano monster curve. This might do your head in Imagine that you have a square of paper and a black pen which draws lines with no width.

Is it possible to draw a curve on the paper which leaves it entirely black? I've recently asked this question to several people - who had differing degrees of mathematical aptitude - and each of them has told me that it is impossible.

Perhaps you would too; and indeed quite recently I tried to prove something assuming such a task to be impossible, only to be told that it can be done.

I'll define the curve as the limit of an infinite sequence of curves; the first one looks like this:. Note that the second curve is made up of ten smaller copies of the first and it's three times longer.

So, to construct the third curve, just replace each of these copies of the first curve with suitably scaled down and rotated copies of the second.

Thus the third curve is composed of one hundred copies of the first curve To complete the rest of the sequence, just keep repeating this process it is called fractal iteration.

Such a curve is known as a Peano monster curve. Now have a look at the following picture: 6 7 4 5 8 3 2 9 0 1 Note that this picture numbers the boxes in the same order as the curve passes through them in the second picture.

Ah ha! You can then more accurately determine where the number gets sent to one the third curve by subdividing box d 1 into ten parts again, and of these you know that the image point must lie in box d 2.

If you keep repeating this process, you can determine where a given number get sent to one sucessively finer iterations of the curve to a greater degree of accuracy; because as each time the process is repeated, the boxes get at least four times smaller.

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