Gridder2

Later levels reveal the first derivative, the second derivative, an inverse on a stated branch, and the perpendicular normal at A. The mathematics for the current case stays expanded in its panel; completing a level adds its worked solution.

Choose Start game beneath the board. Each node is the centre of a box reaching 1/8 along each of its four connected edges. Entering the box automatically carries Gridder smoothly to its centre, from any direction. Each tap requests an animated 1/16-edge step. Hold to move smoothly outside the boxes. The speed setting scales with the board size, so journeys take the same time after resizing; horizontal and vertical screen speeds remain equal. Use the resolution sliders to adjust incoming and outgoing halves of node boxes separately. Gridder reaches each node centre before moving on. While travelling vertically, a brief left/right press is remembered until the next node. Close a loop to fill its whole area pale pink. Each function starts with seven lives. Avoid this family’s three monsters: a catch costs one life. Only the head of a long segmented monster can catch you; its trailing body is safe to cross. Gridder looks frightened as enemies approach and relieved when you escape. Gridder swells navy-blue to three times his size over two seconds with a surprised open-mouth expression, decays, then scatters into pieces before resurrection or Game Over. Your marked areas remain. Escape pauses movement, all three enemies, feeding and the capture animation.

Clear-water pools come in different shapes and remove parts of the grid. Gridder and the land monsters follow the remaining edges around each shore. Water cannot be painted or captured. Pools stay away from the function and the discovery target, and the remaining grid always provides a route around them. Larger pools hold two or three pulsing neon leeches: when one flashes a warning ring, move away from the shore before it lunges! A catch costs one life as the leech drags Gridder into the water and drinks his blood. Your marked areas stay saved. The scorpion strikes with its tail.

A shark patrols the largest water pool. Its flashing warning gives you time to escape the shore; a catch costs one life and spreads a red blood tint through that pool. Large centipedes can lay one or two eggs on grid nodes. Eggs hatch after 10 seconds of active play into differently coloured centipedes. Every 60 seconds of active play another insect species enters from a distant border; visiting insects leave after three minutes. Timers stop during pause, capture, resurrection, completed levels and practice mode. The arrival clock carries between levels of this function; Restart resets it. Population limits keep the board playable.

Gridder can enter an edge obstructed by remains. When he meets a piece directly on the path, he strains and sweats while pushing it slowly to the next node, then shoves it aside. You will hear the stone scrape. Nearby off-path pieces are pushed aside on contact, slowing him by 70% for 40 ms. A compact monster chews a piece on its path for four seconds, with eating sounds, then becomes 30% bigger and 2% faster. Each piece multiplies its current size by 1.3. The segmented monster also stops to eat for four seconds, grows two body segments per remnant, and becomes 2% faster. During a capture, bright red blood flows from Gridder into the attacker’s branching neon veins; each drink gradually makes the attacker 15% thicker, and it keeps that growth afterwards. Its legs sweep nearby pieces aside once. Enemy growth carries into the next level; restarting the function resets it.