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The Beauty of Fractals The Beauty of Fractals What is a Fractal? What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same essential form or structure as the whole, except that they are at a different scale and may be slightly deformed. Thus "Fractal Repetition" of pattern and shape. b) Its form is extremely irregular or fragmented, and remains so, whatever the scale of examination. Consider the leaf of the fern as a good example. c) It contains "distinct elements" whose scales are almost infinitely varied and cover a large range. Generation of fractal images employs the usage of mathematical expressions, these often being trigonometric in type, or polynomials and quadratics - containing numerous adjustable variables. There is then performed a sequence of many iterations during which the shapes are ''built'' and colors are introduced by further math' and color filters - these in fact giving a large degree of control to the finished image form, and not just color. In some instances the generated fractal may be enhanced by use of image editing software to add extra material or just make small changes. This display does suffer some loss of resolution due to image compression. The displayed fractal images (landscape format) here are the intellectual copyright property of ACB Systems . We hope you will enjoy them. Click to Click to continue continue ---

The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same

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Page 1: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same

The Beauty of FractalsThe Beauty of Fractals

What is a Fractal?What is a Fractal?

A geometric figure or natural object that combines the following characteristics:-

a) Its parts have the same essential form or structure as the whole, except that they are at a different scale and may be slightly deformed. Thus "Fractal Repetition" of pattern and shape.

b) Its form is extremely irregular or fragmented, and remains so, whatever the scale of examination. Consider the leaf of the fern as a good example.

c) It contains "distinct elements" whose scales are almost infinitely varied and cover a large range.

Generation of fractal images employs the usage of mathematical expressions, these often being trigonometric in type, or polynomials and quadratics - containing numerous adjustable variables. There is then performed a sequence of many iterations during which the shapes are ''built'' and colors are introduced by further math' and color filters - these in fact giving a large degree of control to the finished image form, and not just color.

In some instances the generated fractal may be enhanced by use of image editing software to add extra material or just make small changes. This display does suffer some loss of resolution due to image compression.

The displayed fractal images (landscape format) here are the intellectual copyright property of ACB Systems. We hope you will enjoy them. Click to continueClick to continue ---

Page 2: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 3: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 4: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 5: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 6: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 7: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 8: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 9: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 10: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 11: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 12: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 13: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 14: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 15: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 16: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 17: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 18: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 19: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 20: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 21: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 22: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 23: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 24: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 25: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 26: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 27: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 28: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 29: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 30: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 31: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 32: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 33: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 34: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 35: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 36: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 37: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 38: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 39: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 40: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 41: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 42: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 43: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 44: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 45: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 46: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 47: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 48: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 49: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 50: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 51: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 52: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 53: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 54: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 55: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 56: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 57: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 58: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 59: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 60: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 61: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 62: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 63: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 64: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
Page 65: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same
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Page 67: The Beauty of Fractals What is a Fractal? A geometric figure or natural object that combines the following characteristics:- a) Its parts have the same

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