How can make this microstructure deformed using the deformation matrix?

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Hello.
I have solved an equation and the below image(256*256) is obtained by using the matrix (phi). I need to achieved a deformed microstructure by using the epsilon=0.2.
For example an microstructure such as the fig.5 be achieved as shown in the attached paper.
I'd be appreciated to solve this.
Thanks.

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