Create a modern and stylish logo for a designer app that incorporates a minimalistic palette of black and white. The design should feature an abstract representation of a stylus or pencil integrated with a digital interface element, such as a pixel or screen outline. The overall shape should be sleek and dynamic, conveying creativity and innovation. Include subtle geometric patterns in the background to add depth, maintaining a balance between simplicity and sophistication.

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Create a modern and stylish logo for a designer app that incorporates a minimalistic palette of black and white. The design should feature an abstract representation of a stylus or pencil integrated with a digital interface element, such as a pixel or screen outline. The overall shape should be sleek and dynamic, conveying creativity and innovation. Include subtle geometric patterns in the background to add depth, maintaining a balance between simplicity and sophistication.