rendering the mandelbrot set on a gpu

i built a mandelbrot set renderer in cuda to see how much faster gpu parallelism is compared to cpu-based approaches like pthreads and openmp. the answer: a lot

the numbers

cuda comes in at ~1.8x faster than openmp and ~5x faster than pthreads — and this is on a relatively simple fractal. the gap only grows with more complex computations

why gpus are good at this

the mandelbrot set is an embarrassingly parallel problem. every pixel is independent — you just iterate z = z² + c until it escapes or hits the max iteration count. no pixel depends on any other pixel

cpus are great at complex, branching, sequential logic. but when you have 2 million pixels that all need the same computation? that's what gpus were designed for

how it works

the kernel launches a 60×34 grid of 32×32 thread blocks — enough to cover every pixel in a 1920×1080 image. each thread:

1. maps its (x, y) position to a point on the complex plane (real: [-2.0, 1.0], imaginary: [-0.85, 0.8375])
2. iterates z = z² + c up to 1000 times
3. bails out early if |z| > 2.0 (the point has escaped)
4. uses logarithmic smoothing on the escape time to avoid banding artifacts
5. maps the smoothed value to an rgb color using a polynomial gradient

the coloring is the fun part — a (1-t)^n * t polynomial for each channel creates that smooth blue-to-gold-to-dark gradient you see in the image

what i learned

• stb_image_write is great for quick image output in c without pulling in a massive library
• cuda's __device__ functions make it easy to break gpu code into clean helper functions
• learning actually how a gpu is faster than a cpu was pretty cool — understanding that gpu's are better for same operation in parallel across threads is cool
• understanding what cuda_device_synchronize does helped me make connections between regular c and cuda or cpu to gpu

what to improve

• someone contacted me on linkedin about using a custom meta library called delresto for optimized cpu performance — it's been a while since the og post, but it's something i want to work on and get back to contacting this researcher i shall leave unnamed

the full source is on github if you want to poke around or run it yourself