Zoom into the Mandelbrot set far past ordinary number precision, and watch each view sharpen as the calculation continues.
Loading the explorer…
Loading the explorer…
Drag to pan. Tap or click the image, then scroll or double click to zoom toward a point. On touch screens, drag with one finger and pinch with two. With the image focused, arrow keys pan, + and − zoom, and R returns to the overview.
Auto uses the GPU when the device passes its start-up check, and the CPU otherwise.
Reuses nearby reference calculations after small moves. Leave this on unless you are comparing results.
Diagnostics
No calculation yet.
Each link opens that view in the explorer above. Shallow locations finish in seconds. Deep locations need many more calculations per pixel and can take minutes.
The main heart-shaped body is the cardioid. The round shapes attached to it are bulbs. All the detail lives on the boundary between the coloured outside and the dark inside.
What to notice: pick any edge and zoom in. Smooth areas stay smooth, edges keep producing new shapes.
Open the whole setThe narrow gap between the main cardioid and the large bulb on its left.
What to notice: curled tails that look like seahorses, lined up along both sides of the valley.
Open Seahorse ValleyThe gap on the right side of the main cardioid, near its cusp.
What to notice: rows of thick trunk shapes that curl inward. Compare them with the thinner Seahorse Valley tails.
Open Elephant ValleyThe thin spike that runs left from the main body along the real axis.
What to notice: a small copy of the whole set sits on the antenna. The thin threads that connect it can vanish at low detail, so raise Detail if the copy looks isolated.
Open the antennaA closer view inside Seahorse Valley.
What to notice: double spirals that wind into a centre point, with smaller spirals branching off their arms.
Open the spiralsThe point where the large left bulb meets the next smaller bulb on the real axis.
What to notice: each bulb along the axis is smaller than the last. Points in each one settle into a cycle twice as long as the one before.
Open the boundaryA published deep location from the rust-fractal project, near the antenna. It uses a budget of 35,494 iterations.
What to notice: filaments and spirals much like those near the surface, at a scale far below what ordinary 64-bit numbers can represent.
Open the 10¹¹³ viewA published deep location from the rust-fractal project, near the top of the set. It uses a budget of 212,138 iterations.
What to notice: how long it takes. Most pixels need over a hundred thousand steps, so expect the image to fill in slowly.
Open the 10³¹⁸ viewA published deep location from the rust-fractal project, on the far left antenna. Its centre is written with over a thousand digits.
What to notice: the structure still looks like the Mandelbrot set. Use Back to return to the surface.
Open the 10¹⁰⁰⁰ viewEach pixel is a number c. The explorer repeats z² + c from zero and counts the steps until the value grows past a fixed size. Points that never grow belong to the set. The boundary between the two is where the spirals, valleys and small copies of the whole set appear.
Colour shows how many steps a point took to escape. Bands close together mean the escape speed changes quickly, which happens near the boundary. Changing the palette recolours the finished pixels without calculating them again.
Dark pixels did not escape within the chosen Detail budget. They may be inside the set, or they may need more steps. Raise Detail to find out. Grey pixels are still being calculated. A few pixels need a slower, more precise check because the fast calculation was not accurate enough there. On the GPU they show an estimated colour until the check finishes; on the processor they are pale pink. Both usually clear within moments.
Ordinary 64-bit numbers run out of precision after about 10¹⁴ magnification. This explorer keeps exact decimal coordinates and uses high-precision reference points, so it can go much deeper. The practical limit is time: deeper views need more steps per pixel and more reference work. Auto uses the GPU when the device passes a start-up check. On our test machine the GPU finished every test view faster than the processor, by 25% to many times over. If a view cannot be finished on the GPU, the processor takes over.