Create Sierpinski's Gasket fractal antenna on X-Y plane


The fractalGasket object creates an equilateral triangle-shaped Sierpinski's Gasket fractal antenna. These fractals are used in building communications systems, wireless networks, universal tactic communications systems, mobile devices, telematics, and radio frequency identification (RFID) antennas.

A fractal antenna uses a self-similar design to maximize the length or increase the perimeter of a material that transmits or receives electromagnetic radiation within a given volume or area. The main advantage of fractal antennas is that they are compact, which is important requirement for small and complex circuits. Fractal antennas also have more input impedance or resistance due to increased length or perimeter.

All fractal antennas are printed structures that are etched on a dielectric substrate.



ant = fractalGasket creates an equilateral triangle-shaped Sierpinski’s gasket fractal antenna. The default planar fractal antenna is in the shape of a bowtie which is center-fed. The antenna resonates at a frequency of 1.3 GHz.


ant = fractalGasket(Name,Value) sets properties using one or more name-value pairs. For example, ant = fractalGasket('Numiterations',4) creates a Sierpinski's Gasket with four iterations.

Output Arguments

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Sierpinski's Gasket fractal antenna, returned as a fractalGasket object.


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Number of iterations of the fractal antenna, specified as a scalar integer.

Example: 'NumIterations',2

Example: ant.NumIterations = 2

Data Types: double

Lengths for three sides of the triangle, specified as a scalar in meters or a two- or three-element vector in meters.

  • Scalar – The triangle is equilateral.

  • Two-element vector – The first value specifies the base of the triangle along the X-axis. The second value specifies the other two sides of the triangle. The triangle is isosceles.

  • Three-element vector – The first value specifies the base of the triangle along the X-axis. The remaining two values specify the other two sides of the triangle. The triangle is scalene.

Example: 'Side',[0.5000,1.000]

Example: ant.Side = [0.5000,1.000]

Data Types: double

Width at the neck of the fractal antenna where the feed is located, specified as a positive scalar integer in meters.

Example: 'NeckWidth',0.0050

Example: ant.NeckWidth = 0.0050

Data Types: double

Lumped elements added to the antenna feed, specified as a lumped element object handle. You can add a load anywhere on the surface of the antenna. By default, the load is at the origin. For more information, see lumpedElement.

Example: 'Load',lumpedelement. lumpedelement is the object handle for the load created using lumpedElement.

Example: ant.Load = lumpedElement('Impedance',75)

Tilt angle of the antenna, specified as a scalar or vector with each element unit in degrees. For more information, see Rotate Antennas and Arrays.

Example: 'Tilt',90

Example: 'Tilt',[90 90],'TiltAxis',[0 1 0;0 1 1] tilts the antenna at 90 degree about two axes, defined by vectors.

Data Types: double

Tilt axis of the antenna, specified as:

  • Three-element vectors of Cartesian coordinates in meters. In this case, each vector starts at the origin and lies along the specified points on the X-, Y-, and Z-axes.

  • Two points in space, each specified as three-element vectors of Cartesian coordinates. In this case, the antenna rotates around the line joining the two points in space.

  • A string input describing simple rotations around one of the principal axes, 'X', 'Y', or 'Z'.

For more information, see Rotate Antennas and Arrays.

Example: 'TiltAxis',[0 1 0]

Example: 'TiltAxis',[0 0 0;0 1 0]

Example: ant.TiltAxis = 'Z'

Object Functions

showDisplay antenna or array structure; Display shape as filled patch
axialRatioAxial ratio of antenna
beamwidthBeamwidth of antenna
chargeCharge distribution on metal or dielectric antenna or array surface
currentCurrent distribution on metal or dielectric antenna or array surface
designDesign prototype antenna or arrays for resonance at specified frequency
EHfieldsElectric and magnetic fields of antennas; Embedded electric and magnetic fields of antenna element in arrays
impedanceInput impedance of antenna; scan impedance of array
meshMesh properties of metal or dielectric antenna or array structure
meshconfigChange mesh mode of antenna structure
patternRadiation pattern and phase of antenna or array; Embedded pattern of antenna element in array
patternAzimuthAzimuth pattern of antenna or array
patternElevationElevation pattern of antenna or array
returnLossReturn loss of antenna; scan return loss of array
sparametersS-parameter object
vswrVoltage standing wave ratio of antenna


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Create and view a default fractal Sierpinski's Gasket.

ant = fractalGasket
ant = 
  fractalGasket with properties:

    NumIterations: 2
             Side: 0.2000
        NeckWidth: 0.0020
             Tilt: 0
         TiltAxis: [1 0 0]
             Load: [1x1 lumpedElement]


Introduced in R2018b