SPIROGRAPHS
A Spirograph is a geometric drawing toy that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids. It was developed by British engineer Denys Fisher and first sold in 1965. "Spirograph" has also been used to describe a variety of software applications that display similar curves. It has also been applied to the class of curves that can be produced with the drawing equipment, and therefore may be regarded as a synonym of hypotrochoids. The name has been a registered trademark of Hasbro, Inc., since it bought the Denys Fisher company.
The original US-released Spirograph consisted of two different-sized plastic rings, with gear teeth on both the inside and outside of their circumferences. They were pinned to a cardboard backing with pins, and any of several provided gearwheels, which had holes provided for a ballpoint pen to extend through them to an underlying paper writing surface. It could be spun around to make geometric shapes on the underlying paper medium. Later, the Super-Spirograph consisted of a set of plastic gears and other interlocking shape-segments such as rings, triangles, or straight bars. It has several sizes of gears and shapes, and all edges have teeth to engage any other piece. For instance, smaller gears fit inside the larger rings, but also can engage the outside of the rings in such a fashion that they rotate around the inside or along the outside edge of the rings.
The original US-released Spirograph consisted of two different-sized plastic rings, with gear teeth on both the inside and outside of their circumferences. They were pinned to a cardboard backing with pins, and any of several provided gearwheels, which had holes provided for a ballpoint pen to extend through them to an underlying paper writing surface. It could be spun around to make geometric shapes on the underlying paper medium. Later, the Super-Spirograph consisted of a set of plastic gears and other interlocking shape-segments such as rings, triangles, or straight bars. It has several sizes of gears and shapes, and all edges have teeth to engage any other piece. For instance, smaller gears fit inside the larger rings, but also can engage the outside of the rings in such a fashion that they rotate around the inside or along the outside edge of the rings.
REPEAT PATTERNS
Repeat patterns are also known as translation patterns and are rigid elements where the motif is simply repeated over and over again along a horizontal and vertical line. These elements normally repeat in a predictable manner.
SYMMETRY
Symmetry has two meanings. The first is a vague sense of harmonious and beautiful proportion and balance. The second is an exact mathematical "patterned self-similarity" that can be demonstrated with the rules of a formal system, such asgeometry or physics.
Although these two meanings of "symmetry" can sometimes be told apart, they are related, so they are here discussed together.
The most familiar type of symmetry for many people is geometrical symmetry. A geometric figure (object) has symmetry if there is an isometry that maps the figure onto itself The type of symmetries that are possible for a geometric object depend on the set of geometric transforms available and what object properties should remain unchanged after a transform. Because the composition of two transforms is also a transform and every transform has an inverse transform that undoes it, the set of transforms under which an object is symmetric form a mathematical group.
Reflectional symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection.
In one dimension, there is a point of symmetry about which reflection takes place; in two dimensions there is an axis of symmetry, and in three dimensions there is a plane of symmetry. An object or figure which is indistinguishable from its transformed image is called mirror symmetric.
BLUE PRINT
A blueprint is a reproduction of a technical drawing, documenting an architecture or an engineering design, using a contact print process on light-sensitive sheets. Introduced in the 19th century, the process allowed rapid and accurate reproduction of documents used in construction and industry. The blue-print process was characterized by light colored lines on a blue background, a negative of the original. The process was unable to reproduce color or shades of grey.
Various base materials have been used for blueprints. Paper was a common choice; for more durable prints linen was sometimes used, but with time, the linen prints would shrink slightly.
The process has been largely displaced by the diazo whiteprint process and by large-format xerographic photocopiers, so reproduced drawings are usually called "prints" or just "drawings".In 1861 Alphonse Louis Poitevin, a French chemist, found that ferro-gallate in gum is light sensitive. Light turns this to an insoluble permanent blue. A coating of this chemical on a paper or other base may be used to reproduce an image from a translucent document.
The ferro-gallate is coated onto a paper from aqueous solution and dried. The coating is yellow. In darkness it is stable for up to three days. It is clamped under glass and a light transmitting document in a daylight exposure frame, which is similar to a picture frame. The frame is put out into daylight requiring a minute or two under a bright sun or about ten times this under an overcast sky. Where ultra-violet light is transmitted the coating converts to a stable blue or black dye. The image can be seen forming, when a strong image is seen the frame is brought indoors and the unconverted coating, under the original image, is washed away. The paper is then dried.
The result is a copy of the original image with the clear background area rendered dark blue and the image reproduced as a white line. The image is stable. The contact printing process has the advantage that no large-field optical system is required. A further advantage is that the reproduced document will have the same scale as the original. Another quality is that the dark blue background makes it difficult to add new information to the print (such as recording as-built changes); a blueprint cannot easily be altered -- depending on the situation, this can be either a strength or a drawback. Since the paper is soaked in liquid during processing, a minor change of scale can occur,and the paper can also become brittle. Engineering drawings often are marked to remind users not to rely on the scale of reproductions.
THE GOLDEN RATIO
Some twentieth-century artists and architects, including Le Corbusier and Dalí, have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing.
FRACTALS
A fractal is a mathematical set that typically displays self-similar patterns, which means it is "the same from near as from far". Fractals may be exactly the same at every scale, or, as illustrated in Figure 1, they may be nearly the same at different scales. The concept of fractal extends beyond self-similarity and includes the idea of adetailed pattern repeating itself.
Fractals are distinguished from regular geometric figures by their fractal dimensional scaling. Doubling the edge lengths of a square scales its area by four, which is two to the power of two, because a square is two dimensional. Likewise, if the radius of a sphere is doubled, its volume scales by eight, which is two to the power of three, because a sphere is three-dimensional. If a fractal's one-dimensional lengths are all doubled, the spatial content of the fractal scales by a number which is not an integer. A fractal has a fractal dimension that usually exceeds its topological dimension and may fall between the integers.
As mathematical equations, fractals are usually nowhere differentiable. An infinite fractal curve can be conceived of as winding through space differently from an ordinary line, still being a 1-dimensional line yet having a fractal dimension indicating it also resembles a surface.
GRIDS
In graphic design, a grid is a structure (usually two-dimensional) made up of a series of intersecting straight (vertical, horizontal, and angular) or curved guide lines used to structure content. The grid serves as an armature on which a designer can organize graphic elements (images, glyphs, paragraphs) in a rational, easy to absorb manner. A grid can be use to organize graphic elements in relation to a page, in relation to other graphic elements on the page, or relation to other parts of the same graphic element or shape.
The less common printing term “reference grid,” is an unrelated system with roots in the early days of printing.Before the invention of movable type and printing, simple grids based on optimal proportions had been used to arrange handwritten text on pages. One such system, known as the Villard Diagram, was in use at least since medieval times.
Grid use in web - While grid systems have seen significant use in print media, interest from web developers has only recently seen a resurgence. Website design frameworks producing HTML and CSS had existed for a while before newer frameworks popularised the use of grid-based layouts. Some grid systems specify fixed-width elements with pixels, and some are 'fluid', meaning that they call for page element sizing to be in relative units like percentages, rather than absolute units like pixels or points
In graphic design, a grid is a structure (usually two-dimensional) made up of a series of intersecting straight (vertical, horizontal, and angular) or curved guide lines used to structure content. The grid serves as an armature on which a designer can organize graphic elements (images, glyphs, paragraphs) in a rational, easy to absorb manner. A grid can be use to organize graphic elements in relation to a page, in relation to other graphic elements on the page, or relation to other parts of the same graphic element or shape.
The less common printing term “reference grid,” is an unrelated system with roots in the early days of printing.Before the invention of movable type and printing, simple grids based on optimal proportions had been used to arrange handwritten text on pages. One such system, known as the Villard Diagram, was in use at least since medieval times.
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