Sine & Sketch

Pictures made of pure math.

Write functions and every pixel obeys them. Release thousands of circles whose size and position come from sine and cosine. Or hand over a photo and have it rebuilt from circles. The ways mathematical artist Hamid Naderi Yeganeh makes images, in one studio.

Open the studio Why this exists
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r = 6 cos(kθ)
x 0.00 · y 0.00

Equations

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Procreate (.procreate), Clip Studio (.clip) and Illustrator (.ai) are closed formats with no public spec, so they are not written directly. Use .svg or .pdf for Illustrator and Affinity, and .psd or .ora for layered raster apps.

      

    

  


  

    
Where this comes from

    
One question, and the person who answers it best

    
Sine & Sketch started from a single question: how can a formula hold a whole picture? The best answer I have seen is the work of Hamid Naderi Yeganeh, and this studio takes heavy inspiration from it. His swarms of shapes indexed by k, his networks of functions that decide the colour of every pixel, and his habit of treating each image as a function are the three ideas under everything here. It is a tribute, not a copy. His own formulas are mostly unpublished, so the examples are my attempts at the same idea. If this makes you curious, go and look at his work first.


    

      

        Hamid Naderi Yeganeh standing beside his artwork A Bird in Flight
        

          
The inspiration

          
Hamid Naderi Yeganeh

          
Iranian mathematician and mathematical artist, born in Qom in 1990. He studied at the University of Qom and Sharif University of Technology and has a PhD from University College London. He draws birds, boats, faces, fractals and tessellations using nothing but mathematical formulas. His artwork 9,000 Ellipses was the cover of The American Mathematical Monthly in November 2017.

          
          
Photo: Hamid Naderi Yeganeh, CC BY 4.0, via Wikimedia Commons. Not affiliated with this project.

        

      


      

        Suryansh Mishra
        

          
The builder

          
Suryansh Mishra

          
AI engineer and computer science student at UPES in Delhi NCR, with a minor in AI and ML from IIT Ropar. I build support bots, RAG systems and agents that ship. I also write poetry. I made Sine & Sketch out of curiosity about how Hamid does what he does, and to give other people a place to try the same ideas.