"39 on the Australian Albums Chart, and number 6 on the New Zealand Albums Chart. It contains one song absent from previous albums (""Bleed Together"") which appeared on import copies of the ""Burden in My Hand"" single. The opening track ""Nothing to Say"" was originally not an A-side. It appeared as the B-side to the band's first single ""Hunted Down"" on Sub Pop in 1987. In addition, ""Get on the Snake"" from ""Louder Than Love"" was released as a promo-only single in 1989. Also, the 1990 Sub Pop single ""Room a Thousand Years Wide"" does not appear on ""A-Sides"", nor"
"snowflake. After each iteration, the number of sides of the Koch snowflake increases by a factor of 4, so the number of sides after iterations is given by: If the original equilateral triangle has sides of length , the length of each side of the snowflake after iterations is: the perimeter of the snowflake after iterations is: The Koch curve has an infinite length because the total length of the curve increases by a factor of four thirds with each iteration. Each iteration creates four times as many line segments as in the previous iteration, with the length of each"
"are snowflakes, and are usually the type of ice particle that falls to the ground. Guinness World Records list the world's largest snowflakes as those of January 1887 at Fort Keogh, Montana; allegedly one measured 38 cm (15 inches) wide. The exact details of the sticking mechanism remain a subject of research. Although the ice is clear, scattering of light by the crystal facets and hollows/imperfections mean that the crystals often appear white in color due to diffuse reflection of the whole spectrum of light by the small ice particles. The shape of the snowflake is determined broadly by the"
"a stylized charge, often used to represent winter or winter sports. Three different snowflake symbols are encoded in Unicode: ""snowflake"" at U+2744 (❄); ""tight trifoliate snowflake"" at U+2745 (❅); and ""heavy chevron snowflake"" at U+2746 (❆). A selection of photographs taken by Wilson Bentley (1865–1931): Snowflake A snowflake is a single ice crystal that has achieved a sufficient size, and may have amalgamated with others, then falls through the Earth's atmosphere as snow. Each flake nucleates around a dust particle in supersaturated air masses by attracting supercooled cloud water droplets, which freeze and accrete in crystal form. Complex shapes emerge"
"in the same micro-environment does not guarantee that each arm grow the same; indeed, for some crystal forms it does not because the underlying crystal growth mechanism also affects how fast each surface region of a crystal grows. Empirical studies suggest less than 0.1% of snowflakes exhibit the ideal six-fold symmetric shape. Very occasionally twelve branched snowflakes are observed; they maintain the six-fold symmetry. Snowflakes form in a wide variety of intricate shapes, leading to the notion that ""no two are alike"". Although nearly-identical snowflakes have been made in laboratory, they are very unlikely to be found in nature. Initial"
"Snowflake A snowflake is a single ice crystal that has achieved a sufficient size, and may have amalgamated with others, then falls through the Earth's atmosphere as snow. Each flake nucleates around a dust particle in supersaturated air masses by attracting supercooled cloud water droplets, which freeze and accrete in crystal form. Complex shapes emerge as the flake moves through differing temperature and humidity zones in the atmosphere, such that individual snowflakes differ in detail from one another, but may be categorized in eight broad classifications and at least 80 individual variants. The main constituent shapes for ice crystals, from"
"of infinitely many equilateral triangles (see figure). Each side of the green triangle is exactly 1/3 the size of a side of the large blue triangle, and therefore has exactly 1/9 the area. Similarly, each yellow triangle has 1/9 the area of a green triangle, and so forth. Taking the blue triangle as a unit of area, the total area of the snowflake is The first term of this series represents the area of the blue triangle, the second term the total area of the three green triangles, the third term the total area of the twelve yellow triangles, and"
"crystal faces from forming properly or at all. However, when snowflakes crystallize, they do not touch each other. Thus, snowflakes form euhedral, six-sided twinned crystals. In rocks, the presence of euhedral crystals may signify that they formed early in the crystallization of magma or perhaps crystallized in a cavity or vug, without hindrance from other crystals. ""Euhedral"" is derived from the Greek ""eu"" meaning ""well, good"" and ""hedron"" meaning ""shape"". Euhedral crystals have flat faces with sharp angles. The flat faces (also called facets) are oriented in a specific way relative to the underlying atomic arrangement of the crystal: They"
"Hexaflake A hexaflake is a fractal constructed by iteratively exchanging each hexagon by a flake of seven hexagons; it is a special case of the ""n""-flake. A hexaflake has 7 hexagons in its ""n""th iteration, each smaller by 1/3 than the hexagons in the previous iteration. Its exterior boundary is the von Koch flake, and the full boundary contains an infinite number of Koch snowflakes. The Hausdorff dimension of the hexaflake is equal to ln(7)/ln(3), approximately 1.7712. It may also be constructed by projecting the Cantor cube onto the plane orthogonal to its main diagonal. A closely related fractal, the"
"1.7712. The formula_12 is obtained because each iteration has 7 hexagons that are scaled by 1/3. The boundary of a hexaflake is the standard Koch curve of 60 degrees and infinitely many Koch snowflakes are contained within. Also, the projection of the cantor cube onto the plane orthogonal to its main diagonal is a hexaflake. Like the pentaflake, there is also a variation of the hexaflake, called the Sierpinski hexagon, that has no central hexagon. Its Hausdorff dimension equals formula_14 ≈ 1.6309. This variation still contains infinitely many Koch curves of 60 degrees. ""n""-flakes of higher polygons also exist, though"
"rhombus, or triangle is rep-4. The sphinx hexiamond (illustrated above) is rep-4 and rep-9, and is one of few known self-replicating pentagons. The Gosper island is rep-7. The Koch snowflake is irrep-7: six small snowflakes of the same size, together with another snowflake with three times the area of the smaller ones, can combine to form a single larger snowflake. A right triangle with side lengths in the ratio 1:2 is rep-5, and its rep-5 dissection forms the basis of the aperiodic pinwheel tiling. By Pythagoras' theorem, the hypotenuse, or sloping side of the rep-5 triangle, has a length of"
"paper snowflakes by folding a piece of paper several times, cutting out a pattern with scissors and then unfolding it. Snowflakes are also often used as symbols representing winter or cold conditions. For example, snow tires which enhance traction during harsh winter driving conditions are labelled with a snowflake on the mountain symbol. A stylized snowflake has been part of the emblem of the 1968 Winter Olympics, 1972 Winter Olympics, 1988 Winter Olympics, 1998 Winter Olympics and 2002 Winter Olympics. Snowflakes are also seen as a symbol of uniqueness as no two are perfectly identical. In heraldry, the snowflake is"
"points on the Koch snowflake is infinite. No small piece of it is line-like, but rather it is composed of an infinite number of segments joined at different angles. The fractal dimension of a curve can be explained intuitively thinking of a fractal line as an object too detailed to be one-dimensional, but too simple to be two-dimensional. Therefore its dimension might best be described not by its usual topological dimension of 1 but by its fractal dimension, which is often a number between one and two; in the case of the Koch snowflake, it is about 1.262. A fractal"
"graupel. Although ice by itself is clear, snow usually appears white in color due to diffuse reflection of the whole spectrum of light by the scattering of light by the small crystal facets of the snowflakes of which it is comprised. The shape of the snowflake is determined broadly by the temperature and humidity at which it is formed. Rarely, at a temperature of around , snowflakes can form in threefold symmetry — triangular snowflakes. The most common snow particles are visibly irregular, although near-perfect snowflakes may be more common in pictures because they are more visually appealing. It is"
"Sierpinski hexagon, is formed by repeatedly replacing each hexagon by six smaller hexagons, omitting the central seventh hexagon. It is named after the work of Wacław Sierpiński and by analogy to the Sierpinski triangle, and has the same Koch snowflake exterior boundary as the hexaflake. The hexaflake has been applied in the design of antennas and optical fibers. Hexaflake A hexaflake is a fractal constructed by iteratively exchanging each hexagon by a flake of seven hexagons; it is a special case of the ""n""-flake. A hexaflake has 7 hexagons in its ""n""th iteration, each smaller by 1/3 than the hexagons"
"N-flake An ""n""-flake, polyflake, or Sierpinski ""n""-gon, is a fractal constructed starting from an ""n""-gon. This ""n""-gon is replaced by a flake of smaller ""n""-gons, such that the scaled polygons are placed at the vertices, and sometimes in the center. This process is repeated recursively to result in the fractal. Typically, there is also the restriction that the ""n""-gons must touch yet not overlap. The most common variety of ""n""-flake is two-dimensional (in terms of its topological dimension) and is formed of polygons. The four most common special cases are formed with triangles, squares, pentagons, and hexagons, but it can"
"since they fall through the atmosphere due to their mass, and may collide and stick together in clusters, or aggregates. These aggregates are usually the type of ice particle that falls to the ground. Guinness World Records lists the world's largest (aggregate) snowflakes as those of January 1887 at Fort Keogh, Montana; allegedly one measured 15 inches (38 cm) wide. Although this report by a farmer is doubtful, aggregates of three or four inches width have been observed. Single crystals the size of a dime (17.91 mm in diameter) have been observed. Snowflakes encapsulated in rime form balls known as"
"perimeter diverges to infinity. Consequently, the snowflake has a finite area bounded by an infinitely long line. The Koch snowflake can be constructed by starting with an equilateral triangle, then recursively altering each line segment as follows: After one iteration of this process, the resulting shape is the outline of a hexagram. The Koch snowflake is the limit approached as the above steps are followed over and over again. The Koch curve originally described by Helge von Koch is constructed with only one of the three sides of the original triangle. In other words, three Koch curves make a Koch"
"thick, and the faceoff spot is a solid blue circle in diameter. All of the other faceoff spots and circles are colored red. Each spot consists of a circle in diameter (as measured from the outermost edges) with an outline thick. Within the spot, two red vertical lines are drawn from the left and right inner edges, and the area between these lines is painted red while the rest of the circle is painted white. At each end of the ice, there is a goal consisting of a metal goal frame and cloth net in which each team must place"
"Mosely snowflake The Mosely snowflake (after Jeannine Mosely) is a Sierpiński–Menger type of fractal obtained in two variants either by the operation opposite to creating the Sierpiński-Menger snowflake or Cantor dust i.e. not by leaving but by removing eight of the smaller 1/3-scaled corner cubes and the central one from each cube left from the previous recursion (lighter) or by removing only corner cubes (heavier). In one dimension this operation (i.e. the recursive removal of two side line segments) is trivial and converges only to single point. It resembles the original water snowflake of snow. By the construction the Hausdorff"
"The Koch snowflake is self-replicating with six copies around a central point and one larger copy at the center. Hence it is an irreptile which is irrep-7. The fractal dimension of the Koch curve is ≈ 1.26186. This is greater than the dimension of a line (1) but less than Peano's space-filling curve (2). The Koch curve is continuous everywhere but differentiable nowhere. It is possible to tessellate the plane by copies of Koch snowflakes in two different sizes. However, such a tessellation is not possible using only snowflakes of one size. Since each Koch snowflake in the tessellation can"
"adiabatic cooling, and ultimately condensation and precipitation. Moisture is removed by orographic lift, leaving drier, warmer air on the descending, leeward side. The resulting enhanced productivity of snow fall and the decrease in temperature with elevation means that snow depth and seasonal persistence of snowpack increases with elevation in snow-prone areas. A snowflake consists of roughly 10 water molecules, which are added to its core at different rates and in different patterns, depending on the changing temperature and humidity within the atmosphere that the snowflake falls through on its way to the ground. As a result, snowflakes vary among themselves,"
"they are less common and don't usually have a central polygon. Some examples are shown below; the 7-flake through 12-flake. While it may not be obvious, these higher polyflakes still contain infinitely many Koch curves, but the angle of the Koch curves decreases as ""n"" increases. Their Hausdorff dimensions are slightly more difficult to calculate than lower ""n""-flakes because their scale factor is less obvious. However, the Hausdorff dimension is always less than two but no less than one. An interesting ""n""-flake is the ∞-flake, because as the value of ""n"" increases, an ""n""-flake's Hausdorff dimension approaches 1, ""n""-flakes can"
"to 2 while the progression for the perimeter diverges to infinity, so as in the case of the Koch snowflake, we have a finite area bounded by an infinite fractal curve. The resulting area fills a square with the same center as the original, but twice the area, and rotated by radians, the perimeter touching but never overlapping itself. The total area covered at the th iteration is: while the total length of the perimeter is: which approaches infinity as increases. Koch snowflake The Koch snowflake (also known as the Koch curve, Koch star, or Koch island) is a mathematical"
"the face-off may be in the circle. A common formation, especially at centre ice, is for a skater to take the face-off, with the wings lateral to the centre on either side, and the skater, usually a defenseman, behind the player handling the face-off, one toward each side. This is not mandatory, however, and other formations are seen—especially where the face-off is in one of the four corner face-off spots. Face-offs are typically conducted at designated places marked on the ice called ""face-off spots"" or ""dots"". There are nine such spots: two in each attacking zone, two on each end"
"to reach another position; or (≈ 7×10) when mirror images (defined as the same sequence of turns, but from the other end of the snake) are counted as the one position. Rubik's Snake A Rubik's Snake (also Rubik's Twist, Rubik's Transformable Snake, Rubik’s Snake Puzzle) is a toy with 24 wedges that are right isosceles triangular prisms. The wedges are connected by spring bolts, so that they can be twisted, but not separated. By being twisted, the Rubik's Snake can be made to resemble a wide variety of objects, animals, or geometric shapes. Its ""ball"" shape in its packaging is"
"Each hexagonal face contains a centre piece, 6 corner pieces and 6 edge pieces, while each pentagonal face contains a centre piece, 5 corner pieces and 5 edge pieces. The puzzle twists around the faces: each twist rotates one face centre piece and moves all edge and corner pieces surrounding it. The pentagonal faces can be twisted 72° in either direction, while the hexagonal faces can be rotated 120°. The purpose of the puzzle is to scramble the colours, and then restore it to its original state of having one colour per face. The puzzle has 150 movable pieces: 60"
"which combinations may occur, are needle, column, plate, and rime. Snow appears white in color despite being made of clear ice. This is due to diffuse reflection of the whole spectrum of light by the small crystal facets of the snowflakes. Snowflakes nucleate around mineral or organic particles in moisture-saturated, subfreezing air masses. They grow by net accretion to the incipient crystals in hexagonal formations. The cohesive forces are primarily electrostatic. In warmer clouds, an aerosol particle or ""ice nucleus"" must be present in (or in contact with) the droplet to act as a nucleus. The particles that make ice"
"Koch snowflake The Koch snowflake (also known as the Koch curve, Koch star, or Koch island) is a mathematical curve and one of the earliest fractal curves to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled ""On a continuous curve without tangents, constructible from elementary geometry"" (original French title: ""Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire"") by the Swedish mathematician Helge von Koch. The progression for the area of the snowflake converges to times the area of the original triangle, while the progression for the snowflake's"
"two sides. Figure 3 shows the first fold, and figure 4 the result of the first nine folds, which form a spiral. Figures 5-6 show the final folding of the spiral to make a hexagon; in 5, two red faces have been hidden by a valley fold, and in 6, two red faces on the bottom side have been hidden by a mountain fold. After figure 6, the final loose triangle is folded over and attached to the other end of the original strip so that one side is all blue, and the other all orange. Photos 7 and 8"
"so forth. Excluding the initial 1, this series is geometric with constant ratio ""r"" = 4/9. The first term of the geometric series is ""a"" = 3(1/9) = 1/3, so the sum is Thus the Koch snowflake has 8/5 of the area of the base triangle. The convergence of a geometric series reveals that a sum involving an infinite number of summands can indeed be finite, and so allows one to resolve many of Zeno's paradoxes. For example, Zeno's dichotomy paradox maintains that movement is impossible, as one can divide any finite path into an infinite number of steps wherein"
"attempts to find identical snowflakes by photographing thousands of them with a microscope from 1885 onward by Wilson Alwyn Bentley found the wide variety of snowflakes we know about today. Ukichiro Nakaya developed a crystal morphology diagram, relating crystal shape to the temperature and moisture conditions under which they formed, which is summarized in the following table: The shape of a snowflake is determined primarily by the temperature and humidity at which it is formed. The most common snow particles are visibly irregular. Freezing air down to promotes planar crystals (thin and flat). In colder air down to , the"
"formula_8 (golden ratio). The formula_7 is obtained because each iteration has 6 pentagons that are scaled by formula_10. The boundary of a pentaflake is the Koch curve of 72 degrees. There is also a variation of the pentaflake that has no central pentagon. Its Hausdorff dimension equals formula_11 ≈ 1.6723. This variation still contains infinitely many Koch curves, but they are somewhat more visible. A hexaflake, is formed by successive flakes of seven regular hexagons. Each flake is formed by placing a scaled hexagon in each corner and one in the center. Its Hausdorff dimension is equal to formula_12 ≈"