FRACTALS FOR ELECTRONIC APPLICATIONS

More documents

Recommendations

Info

<strong>FRACTALS</strong> The discovery of fractals is usually bestowed upon IBM Researcher Benoit Mandelbrot in 1976. It involved calculations that could only be achieved by an intensive iteration process performed by computers… August 18th, 2006 Fractals for electronic applications Maciej J. Ogorzałek
Fractal – “broken, fragmented, irregular” “I coined fractal from the Latin adjective fractus. The corresponding Latin verb frangere means "to break" to create irregular fragments. It is therefore sensible - and how appropriate for our need ! - that, in addition to "fragmented" (as in fraction or refraction), fractus should also mean "irregular", both meanings being preserved in fragment. ” Benoit Mandelbrot : The fractal Geometry of Nature, 1982 •Euclid geometry: cold and dry •Nature: complex, irregular, fragmented “Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.” We are confronted with „rough” and „smooth” !! August 18th, 2006 Fractals for electronic applications Maciej J. Ogorzałek
Page 1: FRACTALS FOR ELECTRONIC APPLICATION
Page 5 and 6: August 18th, 2006 Fractals for elec
Page 7 and 8: • For a square we have N^2 self-s
Page 9 and 10: Helge von Koch Snowflake • Step O
Page 11 and 12: • Named for Polish mathematician
Page 13 and 14: Sierpinski Chaos Game August 18th,
Page 15 and 16: Sierpinski Chaos Game Fractal dimen
Page 17 and 18: In 3-D3 August 18th, 2006 Fractals
Page 19 and 20: Physical relations for capacitors B
Page 21 and 22: How to create capacitors with large
Page 23 and 24: • a) Micrograph of a cross sectio
Page 25 and 26: • Supercapacitor module for HY-LI
Page 41 and 42: Open problems • Theoretical issue
Page 43 and 44: fractal antenna is an antenna that
Page 53 and 54:
August 18th, 2006 Fractals for elec
Page 55 and 56:
Page 57 and 58:
John Gianvittorio - UCLA August 18t
Page 59 and 60:
Page 61 and 62:
Page 63 and 64:
Fractal Antenna • Practical shrin
Page 65 and 66:
FRACTAL AND SPACE-FILLING TRANSMISS
Page 67 and 68:
Visualization of antenna (the brown
Page 69 and 70:
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
Page 85:
show all

FRACTALS FOR ELECTRONIC APPLICATIONS

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?